# On the $A$-integrability of singular integral transforms

Annales de l'institut Fourier (1984)

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

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topMadan, 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

top- [1]A. B. ALEXANDROV, Mat. Zametki, 30, n° 1 (1981).
- [2]N. BARY, Trigonometric Series, Pergamon, 1964.
- [3]C. FEFFERMAN and E. M. STEIN, Hp spaces of several variables, Acta. Math., 129 (1972), 137-193. Zbl0257.46078MR56 #6263
- [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]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]E. M. STEIN. Singular Integrals and differentiability properties of functions, Princeton University Press (1970). Zbl0207.13501MR44 #7280

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