Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 59, No. 3, pp. 249-266 (2002)

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



Weighted Norm Inequality for the Poisson Integral on the Sphere

Benjamin Bordin, Iara A.A. Fernandes and Sergio A. Tozoni

Instituto de Matemática, Universidade Estadual de Campinas,
Caixa Postal 6065, 13.081-970 Campinas - SP -- BRAZIL
E-mail: bordin@ime.unicamp.br , iara@ime.unicamp.br , tozoni@ime.unicamp.br

Abstract: We obtain, for each $p$, $1<p<\infty$, a necessary and sufficient condition for the Poisson integral of functions defined on the sphere $S^n$, to be bounded from a weighted space $L^p(S^n,Wd\sigma)$ into a space $L^p(\B,\nu)$, where $\sigma$ is the Lebesgue measure on $S^n$ and $\nu$ is a positive measure on the unit ball $\B$ of $\R^{n+1}$.

Keywords: Poisson integral; Carleson condition; homogeneous space; weight; sphere.

Classification (MSC2000): 42B25, 43A85.

Full text of the article:

Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.

© 2002 Sociedade Portuguesa de Matemática
© 2002–2007 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition