Skip to main content Accessibility help

A multiplier inclusion theorem on product domains

  • Odysseas Bakas (a1)


In this note it is shown that the class of all multipliers from the d-parameter Hardy space $H_{{\rm prod}}^1 ({\open T}^d)$ to L2 (𝕋d) is properly contained in the class of all multipliers from L logd/2L (𝕋d) to L2(𝕋d).



Hide All
1.Bakas, O., Variants of the inequalities of Paley and Zygmund, J. Fourier Anal. Appl., to appear,
2.Bañuelos, R. and Moore, C. N., Probabilistic behavior of harmonic functions, Progress in Mathematics, Volume 175 (Birkhäuser, Basel, 1999).
3.Bilyk, D., Roth's orthogonal function method in discrepancy theory and some new connections, in A panorama of discrepancy theory, Lecture Notes in Mathematics, Volume 2107, pp. 71158 (Springer, Cham, 2014).
4.Bonami, A., Étude des coefficients de Fourier des fonctions de L p(G), Ann. Inst. Fourier (Grenoble), 20(2) (1970), 335402.
5.Bourgain, J., Brezis, H. and Mironescu, P., Limiting embedding theorems for W s,p when s↑1 and applications, J. Anal. Math. 87 (2002), 77101.
6.Chang, S.-Y.A., Wilson, J. M. and Wolff, T. H., Some weighted norm inequalities concerning the Schrödinger operators, Comment. Math. Helv. 60(2) (1985), 217246.
7.Demeter, C., Di Plinio, F., Logarithmic L p bounds for maximal directional singular integrals in the plane, J. Geom. Anal. 24(1) (2014), 375416.
8.Fefferman, R., Beijing lectures in harmonic analysis, Annals of Mathematics Studies, Volume 112, pp. 47130 (Princeton University Press, Princeton, NJ, 1986).
9.Fefferman, R. and Pipher, J., Multiparameter operators and sharp weighted inequalities, Amer. J. Math. 119(2) (1997), 337369.
10.Grafakos, L., Classical Fourier analysis, 3rd edn, Graduate Texts in Mathematics, Volume 249 (Springer, New York, 2014).
11.Grafakos, L. and Kalton, N. J., The Marcinkiewicz multiplier condition for bilinear operators, Studia Math. 146(2) (2001), 115156.
12.Jessen, B., Marcinkiewicz, J. and Zygmund, A., Note on the differentiability of multiple integrals, Fund. Math. 25(1) (1935), 217234.
13.Moore, C. N., Some applications of Cauchy integrals on curves, PhD Thesis, University of California, LA, 1986.
14.Oberlin, D. M., Two multiplier theorems for H 1(U 2), Proc. Edinburgh Math. Soc. (2) 22(1) (1979), 4347.
15.Pipher, J., Bounded double square functions, Ann. Inst. Fourier (Grenoble), 36(2) (1986), 6982.
16.Pisier, G., Ensembles de Sidon et processus gaussiens, C. R. Acad. Sci. Paris Sér. A-B 286(15) (1978), A671A674.
17.Pisier, G., Sur l'espace de Banach des séries de Fourier aléatoires presque sûrement continues. Séminaire sur la Géométrie des Espaces de Banach (1977–1978), Exp. No. 17–18, École Polytechnique, Palaiseau, 1978.
18.Rudin, W., Trigonometric series with gaps, J. Math. Mech. 9 (1960), 203227.
19.Seeger, A. and Trebels, W., Low regularity classes and entropy numbers, Arch. Math. (Basel) 92(2) (2009), 147157.
20.Zygmund, A., Trigonometric series, Volumes I, II (Cambridge University Press, Cambridge, 2002).


MSC classification

A multiplier inclusion theorem on product domains

  • Odysseas Bakas (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed