Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6419245 | Journal of Mathematical Analysis and Applications | 2012 | 10 Pages |
Abstract
We introduce the notion of s-Carleson measure (sâ¥1) on a homogeneous tree T and give several characterizations of such measures. In particular, we prove the following discrete version of the extension of Carleson's theorem due to Duren.For p>1and sâ¥1, a finite measure Ïon Tis s-Carleson if and only if there exists C>0such that for all fâLp(âT), âPfâLsp(Ï)â¤CâfâLp(âT),where Pfdenotes the Poisson integral of f.Here, Lp(Ï) is the space of functions g defined on T such that |g|p is integrable with respect to Ï and Lp(âT) is the space of functions f defined on the boundary of T such that |f|p is integrable with respect to the representing measure of the harmonic function 1.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Joel M. Cohen, Flavia Colonna, David Singman,