Transference theory onHardy and Sobolev spaces

Maria Carro; Javier Soria

Colloquium Mathematicae (1997)

  • Volume: 74, Issue: 1, page 47-69
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Carro, Maria, and Soria, Javier. "Transference theory onHardy and Sobolev spaces." Colloquium Mathematicae 74.1 (1997): 47-69. <http://eudml.org/doc/210501>.

@article{Carro1997,
abstract = {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.},
author = {Carro, Maria, Soria, Javier},
journal = {Colloquium Mathematicae},
keywords = {transference theorem; convolution operators; multipliers; de Leeuw type restriction theorem},
language = {eng},
number = {1},
pages = {47-69},
title = {Transference theory onHardy and Sobolev spaces},
url = {http://eudml.org/doc/210501},
volume = {74},
year = {1997},
}

TY - JOUR
AU - Carro, Maria
AU - Soria, Javier
TI - Transference theory onHardy and Sobolev spaces
JO - Colloquium Mathematicae
PY - 1997
VL - 74
IS - 1
SP - 47
EP - 69
AB - 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.
LA - eng
KW - transference theorem; convolution operators; multipliers; de Leeuw type restriction theorem
UR - http://eudml.org/doc/210501
ER -

References

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  1. [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. Zbl0729.43003
  2. [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. Zbl0795.43007
  3. [CT] R. Caballero and A. de la Torre, An atomic theory for ergodic H p spaces, Studia Math. 82 (1985), 39-59. Zbl0593.46046
  4. [CW1] R. Coifman and G. Weiss, Transference Methods in Analysis, CBMS Regional Conf. Ser. in Math. 31, Amer. Math. Soc., 1977. 
  5. [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. Zbl0257.46077
  6. [C] L. Colzani, Fourier transform of distributions in Hardy spaces, Boll. Un. Mat. Ital. A (6) 1 (1982), 403-410. Zbl0505.46030
  7. [D] K. de Leeuw, On L p multipliers, Ann. of Math. 81 (1965), 364-379. 
  8. [HR] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. I, Springer, 1963. 
  9. [M] A. Miyachi, On some Fourier multipliers for H p ( R n ) , J. Fac. Sci. Univ. Tokyo 27 (1980), 157-179. Zbl0433.42019

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