On the A-integrability of singular integral transforms
Annales de l'Institut Fourier, Tome 34 (1984) no. 2, p. 53-62
Dans cet article on étudie les espaces de Hardy de type faible des fonctions harmoniques dans le demi-espace supérieur R + n+1 . On démontre la A-intégrabilité des transformées d’intégrales singulières définies par les noyaux de Calderón-Zygmund. Cela généralise un résultat analogue pour les transformées de Riesz démontré par Alexandrov.
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.
@article{AIF_1984__34_2_53_0,
     author = {Madan, Shobha},
     title = {On the $A$-integrability of singular integral transforms},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {34},
     number = {2},
     year = {1984},
     pages = {53-62},
     doi = {10.5802/aif.963},
     zbl = {0527.46047},
     mrnumber = {86b:44001},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1984__34_2_53_0}
}
Madan, Shobha. On the $A$-integrability of singular integral transforms. Annales de l'Institut Fourier, Tome 34 (1984) no. 2, pp. 53-62. doi : 10.5802/aif.963. http://www.numdam.org/item/AIF_1984__34_2_53_0/

[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. | MR 56 #6263 | Zbl 0257.46078

[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. | MR 82k:60106 | Zbl 0466.31006

[5]P. Sjögren and S. Madan, Poisson Integrals of absolutely continuous and other measures, (1983), to appear in Phil. Proc. Camb. Math. Soc. | Zbl 0523.28005

[6]E. M. Stein. Singular Integrals and differentiability properties of functions, Princeton University Press (1970). | MR 44 #7280 | Zbl 0207.13501