On the A -integrability of singular integral transforms

Shobha Madan

Annales de l'institut Fourier (1984)

  • Volume: 34, Issue: 2, page 53-62
  • ISSN: 0373-0956

Abstract

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In this article we study the weak type Hardy space of harmonic functions in the upper half plane R + n + 1 and we prove the A -integrability of singular integral transforms defined by Calderón-Zygmund kernels. This generalizes the corresponding result for Riesz transforms proved by Alexandrov.

How to cite

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Madan, Shobha. "On the $A$-integrability of singular integral transforms." Annales de l'institut Fourier 34.2 (1984): 53-62. <http://eudml.org/doc/74635>.

@article{Madan1984,
abstract = {In this article we study the weak type Hardy space of harmonic functions in the upper half plane $\{\bf R\}^\{n+1\}_+$ and we prove the $A$-integrability of singular integral transforms defined by Calderón-Zygmund kernels. This generalizes the corresponding result for Riesz transforms proved by Alexandrov.},
author = {Madan, Shobha},
journal = {Annales de l'institut Fourier},
keywords = {A-integrability; singular integral transforms; weak type Hardy spaces of harmonic functions in the upper half plane; A-integrability of singular integral transforms defined by Calderon-Zygmund kernels; Riesz transforms},
language = {eng},
number = {2},
pages = {53-62},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the $A$-integrability of singular integral transforms},
url = {http://eudml.org/doc/74635},
volume = {34},
year = {1984},
}

TY - JOUR
AU - Madan, Shobha
TI - On the $A$-integrability of singular integral transforms
JO - Annales de l'institut Fourier
PY - 1984
PB - Association des Annales de l'Institut Fourier
VL - 34
IS - 2
SP - 53
EP - 62
AB - In this article we study the weak type Hardy space of harmonic functions in the upper half plane ${\bf R}^{n+1}_+$ and we prove the $A$-integrability of singular integral transforms defined by Calderón-Zygmund kernels. This generalizes the corresponding result for Riesz transforms proved by Alexandrov.
LA - eng
KW - A-integrability; singular integral transforms; weak type Hardy spaces of harmonic functions in the upper half plane; A-integrability of singular integral transforms defined by Calderon-Zygmund kernels; Riesz transforms
UR - http://eudml.org/doc/74635
ER -

References

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  1. [1]A. B. ALEXANDROV, Mat. Zametki, 30, n° 1 (1981). 
  2. [2]N. BARY, Trigonometric Series, Pergamon, 1964. 
  3. [3]C. FEFFERMAN and E. M. STEIN, Hp spaces of several variables, Acta. Math., 129 (1972), 137-193. Zbl0257.46078MR56 #6263
  4. [4]R. F. GUNDY, On a theorem of F and M. Riez and an identity of A. Wald, Indiana Univ. Math. J., 30 (1981), 589-605. Zbl0466.31006MR82k:60106
  5. [5]P. SJÖGREN and S. MADAN, Poisson Integrals of absolutely continuous and other measures, (1983), to appear in Phil. Proc. Camb. Math. Soc. Zbl0523.28005
  6. [6]E. M. STEIN. Singular Integrals and differentiability properties of functions, Princeton University Press (1970). Zbl0207.13501MR44 #7280

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