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    This (lowercase (translateProductType product.productType)) has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Sogge, Christopher D. Xi, Yakun and Xu, Hang 2018. On Instability of the Nikodym Maximal Function Bounds over Riemannian Manifolds. The Journal of Geometric Analysis, Vol. 28, Issue. 3, p. 2886.

    Rüland, Angkana and Salo, Mikko 2018. Exponential instability in the fractional Calderón problem. Inverse Problems, Vol. 34, Issue. 4, p. 045003.

    Wyman, Emmett L. 2018. Looping Directions and Integrals of Eigenfunctions over Submanifolds. The Journal of Geometric Analysis,

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    Fourier Integrals in Classical Analysis
    • Online ISBN: 9781316341186
    • Book DOI: https://doi.org/10.1017/9781316341186
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Book description

This advanced monograph is concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. In particular, the author uses microlocal analysis to study problems involving maximal functions and Riesz means using the so-called half-wave operator. To keep the treatment self-contained, the author begins with a rapid review of Fourier analysis and also develops the necessary tools from microlocal analysis. This second edition includes two new chapters. The first presents Hörmander's propagation of singularities theorem and uses this to prove the Duistermaat–Guillemin theorem. The second concerns newer results related to the Kakeya conjecture, including the maximal Kakeya estimates obtained by Bourgain and Wolff.

Reviews

Review of previous edition:‘… the book displays an impressive collection of beautiful results on which the book's author and his distinguished collaborators have had a significant influence … The writing is agile and somewhat colloquial, giving a refreshing informal tone to the presentation of quite arduous topics.'

Josefina Alvarez Source: Mathematical Reviews

‘Fourier Integrals and Classical Analysis is an excellent book on a beautiful subject seeing a lot of high-level activity. Sogge notes that the book evolved out of his 1991 UCLA lecture notes, and this indicates the level of preparation expected from the reader: that of a serious advanced graduate student in analysis, or even a beginning licensed analyst, looking to do work in this area. But a lot of advantage can be gained even by fellow travelers, all modulo enough mathematical maturity, training, and Sitzfleisch.’

Michael Berg Source: MAA Reviews

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References
[1] Arnold, V. I. Mathematical methods of classical mechanics, Springer-Verlag, Berlin, 1978.
[1] Avakumovič, V. G. Über die Eigenfunktionen auf geschlossenen Riemannschen Mannigfaltigkeiten, Math. Z. 65 (1956), 327–44.
[1] Beals, M. Lp boundedness of Fourier integral, Mem. Amer.Math. Soc. 264 (1982).
[1] Beals, M., Fefferman, C., and Grossman, R. Strictly pseudoconvex domains in Cn, Notices Amer. Math. Soc. 8 (1983), 125–322.
[1] Bennett, J., Carbery, A, and Tao, T. On the multilinear restriction and Kakeya conjectures, ActaMath. 196 (2006), 261–302.
[1] Bérard, P. Riesz means on Riemannian manifolds, Proc. Symp. Pure Math. XXXVI, American Mathematical Society, Providence, RI, 1980, pp. 1–12.
[2] Bérard, P. On the wave equation on a compact manifold without conjugate points, Math. Z. 155 (1977), 249–76.
[1] Besicovitch, A. S. Sur deux questions d'intégrabilité, J. Soc. Phys.Math. 2 (1919), 105–23.
[2] Besicovitch, A. S. The Kakeya problem, Amer. Math. Monthly 70 (1963), 697–706.
[1] Besse, A. Manifolds all of whose geodesics are closed, Springer-Verlag, Berlin, 1978.
[1] Bonami, A., and Clerc, J. L. Sommes de Cesáro et multiplicateures des développements en harmonics sphériques, Trans. Amer. Math. Soc. 183 (1973), 223–63.
[1] Bourgain, J. Averages in the plane over convex curves and maximal operators, J.Analyse Math. 47 (1986), 69–85.
[2] Bourgain, J. Besicovitch type maximal operators and applications to Fourier analysis, Geom. Funct. Anal. 1 (1991), 147–87.
[3] Bourgain, J. Lp estimates for oscillatory integrals in several variables, Geom. Funct. Anal. 1 (1991), 321–74.
[4] Bourgain, J. On the dimension of Kakeya sets and related maximal inequalities, Geom. Funct. Anal. 9 (1999), 256—282.
[5] Bourgain, J. Harmonic analysis and combinatorics: How much may they contribute to each other?, Mathematics: Frontiers and Perspectives, IMU/Amer. Math. Soc., 2000, pp. 13–32.
[1] Bourgain, J., and Demeter, C. The proof of the ℓ 2 decoupling conjecture, Ann. Math. 182 (2015), 351–89.
[1] Bourgain, J., and Guth, L. Bounds on oscillatory integral operators based on multilinear estimates, Geom. Funct. Anal. 21 (2011), 1239–95.
[1] Calderón A, P. Uniqueness in the Cauchy problem for partial differential equations, Amer. J. Math. 80 (1958), 16–36.
[1] Calderón, A. P., and Zygmund, A. On the existence of certain singular integral operators, Acta Math. 88 (1952), 85–139.
[1] Carbery, A. The boundedness of the maximal Bochner–Riesz operator on L4(R2), Duke Math. J. 50 (1983), 409–16.
[2] Carbery, A. Restriction implies Bochner–Riesz for paraboloids, Proc. Cambridge Phil. Soc. 111 (1992), 525–29.
[1] Carleson, L., and Sjölin, P. Oscillatory integrals and a multiplier problem for the disk, Studia Math. 44 (1972), 287–99.
[1] Christ, F. M. On the almost everywhere convergence of Bochner–Riesz means in higher dimensions, Proc. Amer. Math. Soc. 95 (1985), 16–20.
[2] Christ, F. M. Estimates for the k-plane transform, Indiana Math. J. 33 (1984), 891–910.
[1] Christ, F. M., Duoandikoetxea, J., and Rubio de Francia, J. Maximal operators related to the Radon transform and the Calderón–Zygmund method of rotations, Duke Math. J. 53 (1986), 189–209.
[1] Christ, F. M., and Sogge, C. D. The weak type L1 convergence of eigenfunction expansions for pseudo-differential operators, Invent. Math. 94 (1988), 421–53.
[1] Coifman, R., and Weiss, G. Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569–645.
[1] Colin de Verdiére, Y., and Frisch, M. Régularité Lipschitzienne et solutions de l'équation des ondes sur une variété Riemannienne compacte, Ann. Scient. Ecole Norm. Sup. 9 (1976), 539–65.
[1] Constantin, P., and Saut, J. Local smoothing properties of dispersive equations, J. Amer. Math. Soc. 1 (1988), 413–46.
[1] Córdoba, A. A note on Bochner–Riesz operators, Duke Math. J. 46 (1979), 505–11.
[2] Córdoba, A. Geometric Fourier analysis, Ann. Inst. Fourier 32 (1982), 215–26.
[1] Davies, E. B. Heat kernels and spectral theory, Cambridge University Press, Cambridge, 1989.
[2] Davies, E. B. Spectral properties of compact manifolds and changes of metric, Amer. J. Math. 21 (1990), 15–39.
[1] Davies, R. O. Some remarks on the Kakeya problem, Proc. Cambridge Phil. Soc. 69 (1971), 417–21.
[1] Do Carmo, M. Riemannian geometry, Birkhäuser, Basel, Boston, Berlin, 1992.
[1] Drury, S. Lp estimates for the x-ray transform, Illinois J. Math. 27 (1983), 125–29.
[1] Duistermaat, J. J. Fourier integral operators, Courant Institute of Mathematical Sciences, New York, 1973.
[1] Duistermaat, J. J., and Guillemin, V. W. The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math. 29 (1975), 39–79.
[1] Egorov, Y. P. The canonical transformations of pseudo-differential operators (Russian), Uspehi Mat. Nauk 24,5 (149) (1969), 235–36.
[1] Eskin, G. I. Degenerate elliptic pseudo-differential operators of principal type (Russian), Mat. Sbornik 82 (124) (1970), 585–628; English translation, Math. USSR Sbornik 11 (1970), 539–82.
[1] Falconer, K. J. The geometry of fractal sets, Cambridge University Press, Cambridge, 1985.
[1] Fefferman, C. Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9–36.
[2] Fefferman, C. The multiplier problem for the ball, Ann. Math. 94 (1971), 330–6.
[3] Fefferman, C. A note on spherical summation multipliers, Israel J. Math. 15 (1973), 44–52.
[1] Fefferman, C., and Stein, E. M. Hp spaces of several variables, Acta Math. 129 (1972), 137–93.
[1] Garcia-Cuerva, J., and Rubio de Francia, J, L. Weighted norm inequalities and related topics, North-Holland, Amsterdam, 1985.
[1] Garrigós, G., and Seeger, A. On plate decompositions of cone multipliers, Proc. Edinb. Math. Soc. 52 (2009), no. 3, 631–51.
[1] Gelfand, I. M., and Shilov, G. E. Generalized functions. Volume 1: Properties and operations, Academic Press, New York, 1964.
[1] Ginibre, J., and Velo, G. Generalized Strichartz inequalities for the wave equation, J. Funct. Anal. 133 (1995), 50–68.
[1] Greenleaf, A. Principal curvature and harmonic analysis, Indiana Math. J. 30 (1982), 519–37.
[1] Greenleaf, A., and Uhlmann, G. Estimates for singular Radon transforms and pseudo-differential operators with singular symbols, J. Funct. Anal. 89 (1990), 202–32.
[1] Grieser, D. Lp bounds for eigenfunctions and spectral projections of the Laplacian near a concave boundary. Thesis, UCLA, 1992.
[1] Guillemin, V., and Sternberg, S. Geometric asymptotics, Amer. Math. Soc. Surveys, Providence, RI, 1977.
[1] Hadamard, J. Lectures on Cauchy's problem in linear partial differential equations, Yale University Press, New Haven, CT, 1923.
[1] Hardy, G. H., and Littlewood J, E. Some properties of fractional integrals, I, Math. Z. 27 (1928), 565–606.
[1] Hlawka, E. Über Integrale auf konvexen Körpern I, Monatsh. Math. 54 (1950), 1–36.
[1] Hörmander, L. Estimates for translation invariant operators in Lp spaces, Acta Math. 104 (1960), 93–140.
[2] Hörmander, L. Pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 501–17.
[3] Hörmander, L. On the Riesz means of spectral functions and eigenfunction expansions for elliptic differential operators, Some recent advances in the basic sciences, Yeshiva Univ., New York, 1966.
[4] Hörmander, L. The spectral function of an elliptic operator, ActaMath. 121 (1968), 193–218.
[5] Hörmander, L. Fourier integral operators I, Acta Math. 127 (1971), 79–183.
[6] Hörmander, L. Oscillatory integrals and multipliers on FLp, Ark.Mat. 11 (1971), 1–11.
[7] Hörmander, L. The analysis of linear partial differential operators Volumes I–IV, Springer-Verlag, Berlin, 1983, 1985.
[8] Hörmander, L. Uniqueness theorems for second order elliptic differential equations, Comm. Partial Differential Equations 8 (1983), 21–64.
[9] Hörmander, L. On the existence and the regularity of solutions of linear pseudo-differential equations, Enseignement Math. 17 (1971), 99–163.
[1] Ivrii, V. The second term of the spectral asymptotics for a Laplace–Beltrami operator on manifolds with boundary (Russian), Funksional. Anal. i Prilozhen. 14 (1980) 25–34.
[1] Jerison, D. Carleman inequalities for the Dirac and Laplace operators and unique continuation, Adv. Math. 63 (1986), 118–34.
[1] Jerison, D., and Kenig, C. E. Unique continuation and absence of positive eigenvalues for Schrödinger operators, Ann. Math. 121 (1985), 463–94.
[1] John, F. Plane waves and spherical means applied to differential equations, Interscience, New York, 1955.
[1] Journé, J.-L., Soffer, A., and Sogge, C. D. Decay estimates for Schrödinger operators, Comm. Pure Appl. Math. 44 (1991), 573–604.
[1] Kakeya, S. Some problems on maximum and minimum regarding ovals, Tohoku Science Reports 6 (1917), 71–88.
[1] Kaneko, M., and Sunouchi, G. On the Littlewood-Paley and Marcinkiewicz functions in higher dimensions, TÔhoku Math. J. 37 (1985), 343–65.
[1] Kapitanskii, L. V. Norm estimates in Besov and Lizorkin–Triebel spaces for the solutions of second-order linear hyperbolic equations, J. SovietMath. 56 (1991), 2347–2389.
[2] Kapitanskii, L. V. The Cauchy problem for the semilinear wave equation. I. (Russian); translated from Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 163 (1987), Kraev. Zadachi Mat. Fiz. i Smezhn. Vopr. Teor. Funktsi 19, 76–104, 188 J. Soviet Math. 49 (1990), no. 5, 1166–1186.
[1] Kato, T. On the Cauchy problem for the (generalized) Kortweg-de Vries equation, Studies in Applied Math., Vol. 8, Academic Press, 1983, pp. 93–128.
[1] Katz, N., Laba, I., and Tao, T. An improved bound on theMinkowski dimension of Besicovitch sets in R3 Ann. Math. 152 (2000), 383–446.
[1] Katz, N., and Tao, T. Bounds on arithmetic projections, and applications to the Kakeya conjecture, Math. Res. Lett. 6 (1999), 625–630.
[2] Katz, N., and Tao, T. New bounds for Kakeya problems, J. Anal. Math. 87 (2002), 231–63.
[1] Keel, T., and Tao, T. Endpoint Strichartz estimates, Amer. J. Math. 120 (1998), 955–80.
[1] Kenig, C. E., Ruiz, A., and Sogge, C. D. Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators, Duke Math. J. 55 (1987), 329–48.
[1] Kenig, C. E., Stanton, R., and Tomas, P. Divergence of eigenfunction expansions, J. Funct. Anal. 46 (1982), 28–44.
[1] Kohn, J. J., and Nirenberg, L. On the algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269–305.
[1] Laba, I., and Wolff, T. A local smoothing estimate in higher dimensions, Dedicated to the memory of Tom Wolff, J. Anal. Math. 88 (2002), 149–71.
[1] Lax, P. D. On Cauchy's problem for hyperbolic equations and the differentiability of solutions of elliptic equations, Comm. Pure Appl. Math. 8 (1955), 615–33.
[2] Lax, P. D. Asymptotic solutions of oscillatory intitial value problems, Duke Math. J. 24 (1957), 627–46.
[1] Lee, S. Linear and bilinear estimates for oscillatory integral operators related to restriction to hypersurfaces, J. Funct. Anal. 241 (2006), 56–98.
[1] Lee, S., and Seeger, A. Lebesgue space estimates for a class of Fourier integral operators associated with wave propagation, Math. Nachr. 286 (2013), 743–55.
[1] Lee, S., and Vargas, A. On the cone multiplier in R3, J. Funct. Anal. 263 (2012), 925–40.
[1] Levitan, B. M. On the asymptotic behavior of the spectral function of a self-adjoint differential equation of second order, Isv. Akad. Nauk SSSR Ser. Mat. 16 (1952), 325–52.
[1] Lindblad, H., and Sogge, C. D. On existence and scattering with minimal regularity for semilinear wave equations, J. Funct. Anal. 130 (1995), 357–426.
[1] Littman, W. Lp → Lq estimates for singular integral operators, Proc. Symp. Pure Appl. Math. Amer. Math. Soc. 23 (1973), 479–81.
[1] Marcinkiewicz, J. Sur l'interpolation d'operations, C. R. Acad. Sci. 208 (1939), 1272–73.
[2] Marcinkiewicz, J. Sur les muliplicateurs dés series de Fourier, Studia Math. 8 (1939), 78–91.
[1] Maslov, V. P. Théorie des perturbations et méthodes asymptotiques, French translation, Dunod, Paris, 1972.
[1] Miao, C., Yang, J., and Zheng, J. On Wolff 's L52 -Kakeya maximal inequality in R3, Forum Math. 27 (2015), 3053–77.
[1] Mihlin, S. G. Multidimensional singular integrals and integral equations, Internat. Series of Monographs in Pure and Applied Math., Volume 83, Pergamon Press, Elmsford, NY, 1965.
[1] Minicozzi, W. H., and Sogge, C. D. Negative results for Nikodym maximal functions and related oscillatory integrals in curved space, Math. Res. Lett. 4 (1997), 221–37.
[1] Miyachi, A. On some estimates for the wave equation in Lp and Hp, J. Fac. Sci. Tokyo 27 (1980), 331–54.
[1] Mockenhaupt, G., Seeger, A., and Sogge, C. D. Wave front sets, local smoothing and Bourgain's circular maximal theorem, Ann. Math. 136 (1992), 207–18.
[2] Mockenhaupt, G., Seeger, A., and Sogge, C. D. Local smoothing of Fourier integral operators and Carleson–Sjölin estimates, J. Amer. Math. Soc. 6 (1993), no. 1, 65–130.
[1] Nikodym, O. Sur la mesure des ensembles plans dont tous les points sont rectilinéairement accessibles, Fund. Math. 10 (1927), 116–68.
[1] Oberlin, D. Convolution estimates for some distributions with singularities on the light cone, Duke Math. J. 59 (1989), 747–58.
[1] Oberlin, D., and Stein, E. M. Mapping properties of the Radon transform, Indiana Math. J. 31 (1982), 641–50.
[1] Pan, Y., and Sogge, C. D. Oscillatory integrals associated to folding canonical relations, Colloquium Mathematicum 60 (1990), 413–19.
[1] Peral, J. Lp estimates for the wave equation, J. Funct. Anal. 36 (1980), 114–45.
[1] Phong, D. H., and Stein, E. M. Hilbert integrals, singular integrals and Radon transforms I, Acta Math. 157 (1986), 99–157.
[1] Riesz, M. Sur les maxima des formes bilinéaires et sur les fonctionnelles linéaires, Acta Math. 49 (1926), 465–97.
[2] Riesz, M. L'intégrale de Reimann-Liouville et le probléme de Cauchy, Acta Math. 81 (1949), 1–223.
[1] Safarov, V. G. Asymptotics of a spectral function of a positive elliptic operator without a nontrapping condition, (Russian) Funktsional. Anal. i Prilozhen. 22 (1988) 53–65, 96; translation in Funct. Anal. Appl. 22 (1989), 213–23
[1] Sato, M. Hyperfunctions and partial differential equations, Proc. Int. Conf. on Funct. Anal. and Rel. Topics, Tokyo University Press (1969), 91–94.
[1] Sawyer, E. Unique continuation for Schrödinger operators in dimensions three or less, Ann. Inst. Fourier (Grenoble) 33 (1984), 189–200.
[1] Seeger, A., and Sogge, C. D. On the boundedness of functions of (pseudo)-differential operators on compact manifolds, Duke Math. J. 59 (1989), 709–36.
[2] Seeger, A., and Sogge, C. D. Bounds for eigenfunctions of differential operators, Indiana Math. J. 38 (1989), 669–82.
[1] Seeger, A., Sogge, C. D., and Stein, E. M. Regularity properties of Fourier integral operators, Ann. Math. 134 (1991), 231–51.
[1] Seeley, R. T. Singular integrals and boundary value problems, Amer. J. Math. 88 (1966), 781–809.
[2] Seeley, R. T. Complex powers of an elliptic operator, Proc. Symp. Pure Math. 10 (1968), 288–307.
[1] Sjölin, P. Regularity of solutions to the Schrödinger equation, Duke Math. J. 55 (1987), 699–715.
[1] Sobolev, S. L. Sur un théorém d'analyse fonctionnelle (Russian; French summary), Mat. Sb. 46 (1938), 471–97.
[1] Sogge, C. D. Oscillatory integrals and spherical harmonics, Duke Math. J. 53 (1986), 43–65.
[2] Sogge, C. D. Concerning the Lp norm of spectral clusters for second order elliptic operators on compact manifolds, J. Funct. Anal. 77 (1988), 123–34.
[3] Sogge, C. D. On the convergence of Riesz means on compact manifolds, Ann. of Math. 126 (1987), 439–47.
[4] Sogge, C. D. Remarks on L2 restriction theorems for Riemannian manifolds, Analysis at Urbana 1, Cambridge University Press, Cambridge, 1989, pp. 416–22.
[5] Sogge, C. D. Oscillatory integrals and unique continuation for second order elliptic differential equations, J. Amer.Math. Soc. 2 (1989), 489–515.
[6] Sogge, C. D. Propagation of singularities and maximal functions in the plane, Invent. Math. 104 (1991), 349–76.
[7] Sogge, C. D. Concerning Nikodym-type sets in 3-dimensional curved spaces, J. Amer. Math. Soc. 12 (1999), 1–31.
[8] Sogge, C. D. Hangzhou lectures on eigenfunctions of the Laplacian, Princeton University Press, Princeton, NJ, 2014.
[1] Sogge, C. D., and Stein, E. M. Averages over hypersurfaces in Rn, Invent. Math. 82 (1985), 543–56.
[2] Sogge, C. D., and Stein, E. M. Averages over hypersurfaces II, Invent. Math. 86 (1986), 233–42.
[3] Sogge, C. D., and Stein, E. M. Averages of functions over hypersurfaces: Smoothness of generalized Radon transforms, J. Analyse Math. 54 (1990), 165–88.
[1] Sogge, C. D., Toth, J. A., and Zelditch, S. About the blowup of quasimodes on Riemannian manifolds, J. Geom. Anal. 21 (2011) 150–73.
[1] Sogge, C. D., and Zelditch, S. Riemannian manifolds with maximal eigenfunction growth, Duke Math. J. 114 (2002), 387–437.
[2] Sogge, C. D., and Zelditch, S. Focal points and sup-norms of eigenfunctions, Rev. Mat. Iberoam, 32 (2016), no. 3, 971–994.
[3] Sogge, C. D., and Zelditch, S. Focal points and sup-norms of eigenfunctions on Riemannian manifolds II: the two-dimensional case, Rev. Mat. Iberoam., 32 (2016), no. 3, 995–999.
[1] Stanton, R., and Weinstein, A. On the L4 norm of spherical harmonics, Math. Proc. Camb. Phil. Soc. 89 (1981), 343–58.
[1] Stein, E. M. Interpolation of linear operators, Trans. Amer. Math. Soc. 83 (1956), 482–92.
[2] Stein, E. M. Singular integrals and differentiablity properties of functions, Princeton University Press, Princeton, NJ, 1970.
[3] Stein, E. M. Maximal functions: spherical means, Proc. Natl. Acad. Sci. USA 73 (1976), 2174–5.
[4] Stein, E. M. Oscillatory integrals in Fourier analysis, Beijing Lectures in Harmonic Analysis, Princeton University Press, Princeton, NJ, 1986, pp. 307–56.
[5] Stein, E. M. Harmonic analysis: Real-variable methods, orthogonality, and oscillatory integrals, Princeton University Press, Princeton, NJ 1993.
[1] Stein, E. M., and Shakarchi, R. Real analysis. Measure theory, integration, and Hilbert spaces. Princeton Lectures in Analysis, III, Princeton University Press, Princeton, NJ, 2005.
[1] Stein, E. M., and Wainger, S. Problems in harmonic analysis related to curvature, Bull. Amer. Math. Soc. 84 (1978), 1239–95.
[1] Stein, E. M., and Weiss, G. Introduction to Fourier analysis on Euclidean spaces, Princeton University Press Princeton, NJ, 1971.
[1] Sternberg, S. Lectures on differential geometry, Chelsea, New York, 1964, 1983.
[1] Strichartz, R. A priori estimates for the wave equation and some applications, J. Funct. Analysis 5 (1970), 218–35.
[2] Strichartz, R. A functional calculus for elliptic pseudo-differential operators, Amer. J. Math. 94 (1972), 711–22.
[3] Strichartz, R. Restriction of Fourier transform to quadratic surfaces, Duke Math. J. 44 (1977), 705–14.
[1] Sugimoto, M. On some Lp-estimates for hyperbolic operators, ArkivMat. 30 (1992), 149–63.
[1] Tao, T. Restriction theorems, Besicovitch sets and applications to PDE, unpublished lecture notes, 1999.
[2] Tao, T. The Bochner–Riesz conjecture implies the restriction conjecture, Duke Math. J. 96 (1999), 263–375.
[3] Tao, T. From rotating needles to stability of waves: Emerging connections between combinatorics, analysis, and PDE, Notices Amer. Math. Soc. 48 (2001), 294–303.
[1] Taylor, M. Fourier integral operators and harmonic analysis on compact manifolds, Proc. Symp. Pure Math. 35 (1979), 115–36.
[2] Taylor, M. Pseudodifferential operators, Princeton University Press, Princeton, NJ, 1981.
[1] Thorin, O. An extension of a convexity theorem due to M. Riesz, Kungl. Fys. Sällsk. Lund. Förh. 8 (1939).
[1] Tomas, P. Restriction theorems for the Fourier transform, Proc. Symp. Pure Math. 35 (1979), 111–14.
[1] Treves, F. Introduction to pseudodifferential and Fourier integral operators. Volume 1: Pseudodifferential operators. Volume 2: Fourier integral operators, Plenum Press, New York and London, 1980.
[1] Vega, L. Schrödinger equations: pointwise convergence to the initial data, Proc. Amer. Math. Soc. 102 (1988), 874–78.
[1] Wiener, N. The ergodic theorem, Duke Math. J. 5 (1939), 1–18.
[1] Wisewell, S. Kakeya sets of curves, Geom. Funct. Anal. 15 (2005), 1319–62.
[1] Wolff, T. Unique continuation for and related problems, Revista Math. Iber. 6 (1990), 155–200.
[2] Wolff, T. A property of measures in Rn and an application to unique continuation, Geom. Funct. Anal. 2 (1992), 225–84.
[3] Wolff, T. An improved bound for Kakeya type maximal functions, Revista Math. 11 (1993) 651–674.
[4] Wolff, T. Recent work connected with the Kakeya problem, Prospects in Mathematics, Princeton, NJ, 1996 AMS, 129–62.
[5] Wolff, T. Local smoothing type estimates on Lp for large p, Geom. Funct. Anal. 10 (2000), 1237–88.
[6] Wolff, T. A sharp bilinear cone restriction estimate Ann. Math. 153 (2001), 661–98.
[7] Wolff, T. Lectures on harmonic analysis. With a foreword by Charles Fefferman and preface by Izabella Laba. Edited by Laba and Carol Shubin University Lecture Series 29, American Mathematical Society, Providence, RI, 2003.
[1] Xi, Y. On Kakeya-Nikodym type maximal inequalities, Trans. Amer. Math. Soc., to appear.
[1] Zygmund, A. On a theorem of Marcinkiewicz concerning interpolation of operators, J. Math. Pure Appl. 35 (1956), 223–48.
[2] Zygmund, A. On Fourier coefficients and transforms of two variables, Studia Math. 50 (1974), 189–201.
[3] Zygmund, A. Trigonometric series, Cambridge University Press, Cambridge, 1979.

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