We show that the transference method of Coifman and Weiss can be extended to Hardy and Sobolev spaces. As an application we obtain the de Leeuw restriction theorems for multipliers.
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, 08071 Barcelona, Spain
Bibliografia
[ABG1] N. Asmar, E. Berkson and T. A. Gillespie, Transference of strong type maximal inequalities by separation-preserving representations, Amer. J. Math. 113 (1991), 47-74.
[ABG2] N. Asmar, E. Berkson and T. A. Gillespie, Transference of weak type maximal inequalities by distributionally bounded representations, Quart. J. Math. Oxford 43 (1992), 259-282.
[CT] R. Caballero and A. de la Torre, An atomic theory for ergodic $H^p$ spaces, Studia Math. 82 (1985), 39-59.
[CW1] R. Coifman and G. Weiss, Transference Methods in Analysis, CBMS Regional Conf. Ser. in Math. 31, Amer. Math. Soc., 1977.
[CW2] R. Coifman and G. Weiss, Maximal functions and $H^p$ spaces defined by ergodic transformations, Proc. Nat. Acad. Sci. U.S.A. 70 (1973), 1761-1763.
[C] L. Colzani, Fourier transform of distributions in Hardy spaces, Boll. Un. Mat. Ital. A (6) 1 (1982), 403-410.
[D] K. de Leeuw, On $L_p$ multipliers, Ann. of Math. 81 (1965), 364-379.
[HR] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. I, Springer, 1963.
[M] A. Miyachi, On some Fourier multipliers for $H^p(\sym R^n)$, J. Fac. Sci. Univ. Tokyo 27 (1980), 157-179.
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Bibliografia
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