[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.CrossRefGoogle Scholar

[1] Beals, M. Lp boundedness of Fourier integral, Mem. Amer.Math. Soc. 264 (1982).Google Scholar

[1] Beals, M., Fefferman, C., and Grossman, R. Strictly pseudoconvex domains in Cn, Notices Amer. Math. Soc. 8 (1983), 125–322.CrossRefGoogle Scholar

[1] Bennett, J., Carbery, A, and Tao, T. On the multilinear restriction and Kakeya conjectures, ActaMath. 196 (2006), 261–302.Google Scholar

[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.Google Scholar

[1] Besicovitch, A. S. Sur deux questions d'intégrabilité, J. Soc. Phys.Math. 2 (1919), 105–23.Google Scholar

[2] Besicovitch, A. S. The Kakeya problem, Amer. Math. Monthly 70 (1963), 697–706.Google Scholar

[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.Google Scholar

[1] Bourgain, J. Averages in the plane over convex curves and maximal operators, J.Analyse Math. 47 (1986), 69–85.CrossRefGoogle Scholar

[2] Bourgain, J. Besicovitch type maximal operators and applications to Fourier analysis, Geom. Funct. Anal. 1 (1991), 147–87.CrossRefGoogle Scholar

[3] Bourgain, J. Lp estimates for oscillatory integrals in several variables, Geom. Funct. Anal. 1 (1991), 321–74.CrossRefGoogle Scholar

[4] Bourgain, J. On the dimension of Kakeya sets and related maximal inequalities, Geom. Funct. Anal. 9 (1999), 256—282.CrossRef

[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.CrossRefGoogle Scholar

[1] Bourgain, J., and Guth, L. Bounds on oscillatory integral operators based on multilinear estimates, Geom. Funct. Anal. 21 (2011), 1239–95.Google Scholar

[1] Calderón A, P. Uniqueness in the Cauchy problem for partial differential equations, Amer. J. Math. 80 (1958), 16–36.CrossRefGoogle Scholar

[1] Calderón, A. P., and Zygmund, A. On the existence of certain singular integral operators, Acta Math. 88 (1952), 85–139.CrossRefGoogle Scholar

[1] Carbery, A. The boundedness of the maximal Bochner–Riesz operator on L4(R2), Duke Math. J. 50 (1983), 409–16.Google Scholar

[2] Carbery, A. Restriction implies Bochner–Riesz for paraboloids, Proc. Cambridge Phil. Soc. 111 (1992), 525–29.Google Scholar

[1] Carleson, L., and Sjölin, P. Oscillatory integrals and a multiplier problem for the disk, Studia Math. 44 (1972), 287–99.Google Scholar

[1] Christ, F. M. On the almost everywhere convergence of Bochner–Riesz means in higher dimensions, Proc. Amer. Math. Soc. 95 (1985), 16–20.CrossRefGoogle Scholar

[2] Christ, F. M. Estimates for the k-plane transform, Indiana Math. J. 33 (1984), 891–910.Google Scholar

[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.Google Scholar

[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.Google Scholar

[1] Coifman, R., and Weiss, G. Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569–645.CrossRefGoogle Scholar

[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.CrossRefGoogle Scholar

[1] Constantin, P., and Saut, J. Local smoothing properties of dispersive equations, J. Amer. Math. Soc. 1 (1988), 413–46.CrossRefGoogle Scholar

[1] Córdoba, A. A note on Bochner–Riesz operators, Duke Math. J. 46 (1979), 505–11.Google Scholar

[2] Córdoba, A. Geometric Fourier analysis, Ann. Inst. Fourier 32 (1982), 215–26.Google Scholar

[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.Google Scholar

[1] Davies, R. O. Some remarks on the Kakeya problem, Proc. Cambridge Phil. Soc. 69 (1971), 417–21.Google Scholar

[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.Google Scholar

[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.CrossRefGoogle Scholar

[1] Egorov, Y. P. The canonical transformations of pseudo-differential operators (Russian), Uspehi Mat. Nauk 24,5 (149) (1969), 235–36.Google Scholar

[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.CrossRefGoogle Scholar

[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.CrossRefGoogle Scholar

[2] Fefferman, C. The multiplier problem for the ball, Ann. Math. 94 (1971), 330–6.Google Scholar

[3] Fefferman, C. A note on spherical summation multipliers, Israel J. Math. 15 (1973), 44–52.CrossRefGoogle Scholar

[1] Fefferman, C., and Stein, E. M. Hp spaces of several variables, Acta Math. 129 (1972), 137–93.CrossRefGoogle Scholar

[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.Google Scholar

[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.Google Scholar

[1] Greenleaf, A. Principal curvature and harmonic analysis, Indiana Math. J. 30 (1982), 519–37.Google Scholar

[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.Google Scholar

[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.CrossRefGoogle Scholar

[1] Hlawka, E. Über Integrale auf konvexen Körpern I, Monatsh. Math. 54 (1950), 1–36.Google Scholar

[1] Hörmander, L. Estimates for translation invariant operators in Lp spaces, Acta Math. 104 (1960), 93–140.CrossRefGoogle Scholar

[2] Hörmander, L. Pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 501–17.CrossRefGoogle Scholar

[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.Google Scholar

[5] Hörmander, L. Fourier integral operators I, Acta Math. 127 (1971), 79–183.CrossRefGoogle Scholar

[6] Hörmander, L. Oscillatory integrals and multipliers on FLp, Ark.Mat. 11 (1971), 1–11.CrossRefGoogle Scholar

[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.Google Scholar

[9] Hörmander, L. On the existence and the regularity of solutions of linear pseudo-differential equations, Enseignement Math. 17 (1971), 99–163.Google Scholar

[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.Google Scholar

[1] Jerison, D. Carleman inequalities for the Dirac and Laplace operators and unique continuation, Adv. Math. 63 (1986), 118–34.CrossRef

[1] Jerison, D., and Kenig, C. E. Unique continuation and absence of positive eigenvalues for Schrödinger operators, Ann. Math. 121 (1985), 463–94.CrossRefGoogle Scholar

[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.Google Scholar

[1] Kakeya, S. Some problems on maximum and minimum regarding ovals, Tohoku Science Reports 6 (1917), 71–88.Google Scholar

[1] Kaneko, M., and Sunouchi, G. On the Littlewood-Paley and Marcinkiewicz functions in higher dimensions, TÔhoku Math. J. 37 (1985), 343–65.Google Scholar

[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.Google Scholar

[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.Google Scholar

[1] Katz, N., and Tao, T. Bounds on arithmetic projections, and applications to the Kakeya conjecture, Math. Res. Lett. 6 (1999), 625–630.CrossRefGoogle Scholar

[2] Katz, N., and Tao, T. New bounds for Kakeya problems, J. Anal. Math. 87 (2002), 231–63.CrossRefGoogle Scholar

[1] Keel, T., and Tao, T. Endpoint Strichartz estimates, Amer. J. Math. 120 (1998), 955–80.CrossRefGoogle Scholar

[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.Google Scholar

[1] Kenig, C. E., Stanton, R., and Tomas, P. Divergence of eigenfunction expansions, J. Funct. Anal. 46 (1982), 28–44.CrossRefGoogle Scholar

[1] Kohn, J. J., and Nirenberg, L. On the algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269–305.CrossRefGoogle Scholar

[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.CrossRefGoogle Scholar

[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.CrossRefGoogle Scholar

[2] Lax, P. D. Asymptotic solutions of oscillatory intitial value problems, Duke Math. J. 24 (1957), 627–46.Google Scholar

[1] Lee, S. Linear and bilinear estimates for oscillatory integral operators related to restriction to hypersurfaces, J. Funct. Anal. 241 (2006), 56–98.CrossRefGoogle Scholar

[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.Google Scholar

[1] Lee, S., and Vargas, A. On the cone multiplier in R3, J. Funct. Anal. 263 (2012), 925–40.CrossRefGoogle Scholar

[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.Google Scholar

[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.Google Scholar

[1] Littman, W. Lp → Lq estimates for singular integral operators, Proc. Symp. Pure Appl. Math. Amer. Math. Soc. 23 (1973), 479–81.CrossRefGoogle Scholar

[1] Marcinkiewicz, J. Sur l'interpolation d'operations, C. R. Acad. Sci. 208 (1939), 1272–73.Google Scholar

[2] Marcinkiewicz, J. Sur les muliplicateurs dés series de Fourier, Studia Math. 8 (1939), 78–91.CrossRef

[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.Google Scholar

[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.CrossRefGoogle Scholar

[1] Miyachi, A. On some estimates for the wave equation in Lp and Hp, J. Fac. Sci. Tokyo 27 (1980), 331–54.Google Scholar

[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.CrossRefGoogle Scholar

[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.Google Scholar

[1] Nikodym, O. Sur la mesure des ensembles plans dont tous les points sont rectilinéairement accessibles, Fund. Math. 10 (1927), 116–68.Google Scholar

[1] Oberlin, D. Convolution estimates for some distributions with singularities on the light cone, Duke Math. J. 59 (1989), 747–58.Google Scholar

[1] Oberlin, D., and Stein, E. M. Mapping properties of the Radon transform, Indiana Math. J. 31 (1982), 641–50.Google Scholar

[1] Pan, Y., and Sogge, C. D. Oscillatory integrals associated to folding canonical relations, Colloquium Mathematicum 60 (1990), 413–19.Google Scholar

[1] Peral, J. Lp estimates for the wave equation, J. Funct. Anal. 36 (1980), 114–45.Google Scholar

[1] Phong, D. H., and Stein, E. M. Hilbert integrals, singular integrals and Radon transforms I, Acta Math. 157 (1986), 99–157.CrossRefGoogle Scholar

[1] Riesz, M. Sur les maxima des formes bilinéaires et sur les fonctionnelles linéaires, Acta Math. 49 (1926), 465–97.CrossRefGoogle Scholar

[2] Riesz, M. L'intégrale de Reimann-Liouville et le probléme de Cauchy, Acta Math. 81 (1949), 1–223.CrossRefGoogle Scholar

[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), 213–23Google Scholar

[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.Google Scholar

[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.Google Scholar

[2] Seeger, A., and Sogge, C. D. Bounds for eigenfunctions of differential operators, Indiana Math. J. 38 (1989), 669–82.CrossRefGoogle Scholar

[1] Seeger, A., Sogge, C. D., and Stein, E. M. Regularity properties of Fourier integral operators, Ann. Math. 134 (1991), 231–51.CrossRefGoogle Scholar

[1] Seeley, R. T. Singular integrals and boundary value problems, Amer. J. Math. 88 (1966), 781–809.CrossRefGoogle Scholar

[2] Seeley, R. T. Complex powers of an elliptic operator, Proc. Symp. Pure Math. 10 (1968), 288–307.Google Scholar

[1] Sjölin, P. Regularity of solutions to the Schrödinger equation, Duke Math. J. 55 (1987), 699–715.Google Scholar

[1] Sobolev, S. L. Sur un théorém d'analyse fonctionnelle (Russian; French summary), Mat. Sb. 46 (1938), 471–97.Google Scholar

[1] Sogge, C. D. Oscillatory integrals and spherical harmonics, Duke Math. J. 53 (1986), 43–65.CrossRefGoogle Scholar

[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.CrossRefGoogle Scholar

[3] Sogge, C. D. On the convergence of Riesz means on compact manifolds, Ann. of Math. 126 (1987), 439–47.Google Scholar

[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.CrossRefGoogle Scholar

[6] Sogge, C. D. Propagation of singularities and maximal functions in the plane, Invent. Math. 104 (1991), 349–76.Google Scholar

[7] Sogge, C. D. Concerning Nikodym-type sets in 3-dimensional curved spaces, J. Amer. Math. Soc. 12 (1999), 1–31.CrossRef

[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.CrossRefGoogle Scholar

[2] Sogge, C. D., and Stein, E. M. Averages over hypersurfaces II, Invent. Math. 86 (1986), 233–42.Google Scholar

[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.Google Scholar

[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.CrossRefGoogle Scholar

[1] Sogge, C. D., and Zelditch, S. Riemannian manifolds with maximal eigenfunction growth, Duke Math. J. 114 (2002), 387–437.Google Scholar

[2] Sogge, C. D., and Zelditch, S. Focal points and sup-norms of eigenfunctions, Rev. Mat. Iberoam, 32 (2016), no. 3, 971–994.Google Scholar

[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.Google Scholar

[1] Stanton, R., and Weinstein, A. On the L4 norm of spherical harmonics, Math. Proc. Camb. Phil. Soc. 89 (1981), 343–58.Google Scholar

[1] Stein, E. M. Interpolation of linear operators, Trans. Amer. Math. Soc. 83 (1956), 482–92.Google Scholar

[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.Google Scholar

[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.Google Scholar

[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.Google Scholar

[2] Strichartz, R. A functional calculus for elliptic pseudo-differential operators, Amer. J. Math. 94 (1972), 711–22.Google Scholar

[3] Strichartz, R. Restriction of Fourier transform to quadratic surfaces, Duke Math. J. 44 (1977), 705–14.Google Scholar

[1] Sugimoto, M. On some Lp-estimates for hyperbolic operators, ArkivMat. 30 (1992), 149–63.Google Scholar

[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.Google Scholar

[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.Google Scholar

[1] Taylor, M. Fourier integral operators and harmonic analysis on compact manifolds, Proc. Symp. Pure Math. 35 (1979), 115–36.Google Scholar

[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).Google Scholar

[1] Tomas, P. Restriction theorems for the Fourier transform, Proc. Symp. Pure Math. 35 (1979), 111–14.CrossRefGoogle Scholar

[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.CrossRef

[1] Vega, L. Schrödinger equations: pointwise convergence to the initial data, Proc. Amer. Math. Soc. 102 (1988), 874–78.Google Scholar

[1] Wiener, N. The ergodic theorem, Duke Math. J. 5 (1939), 1–18.Google Scholar

[1] Wisewell, S. Kakeya sets of curves, Geom. Funct. Anal. 15 (2005), 1319–62.Google Scholar

[1] Wolff, T. Unique continuation for and related problems, Revista Math. Iber. 6 (1990), 155–200.CrossRefGoogle Scholar

[2] Wolff, T. A property of measures in Rn and an application to unique continuation, Geom. Funct. Anal. 2 (1992), 225–84.Google Scholar

[3] Wolff, T. An improved bound for Kakeya type maximal functions, Revista Math. 11 (1993) 651–674.Google Scholar

[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.CrossRefGoogle Scholar

[6] Wolff, T. A sharp bilinear cone restriction estimate Ann. Math. 153 (2001), 661–98.Google Scholar

[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.Google Scholar

[2] Zygmund, A. On Fourier coefficients and transforms of two variables, Studia Math. 50 (1974), 189–201.CrossRefGoogle Scholar

[3] Zygmund, A. Trigonometric series, Cambridge University Press, Cambridge, 1979.