Carleson measures on a homogeneous tree

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:395

Article

Cohen, Joel M.²  Colonna, Flavia¹  Singman, David¹ 

[1] George Mason Univ, Dept Math Sci, Fairfax, VA 22030 USA

[2] Univ Maryland, Dept Math, College Pk, MD 20742 USA

关键词: Carleson measures;    Trees;    Hardy spaces;    Harmonic;    Poisson kernel;   

DOI  :  10.1016/j.jmaa.2012.05.052

来源: Elsevier

【 摘 要 】

We introduce the notion of s-Carleson measure (s >= 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 > 1 and s >= 1, a finite measure sigma on T is s-Carleson if and only if there exists C > 0 such that for all f is an element of L-p(partial derivative T), parallel to Pf parallel to(Lsp(sigma)) <= C parallel to f parallel to(Lp(partial derivative T)), where Pf denotes the Poisson integral of f. Here, L-p(sigma) is the space of functions g defined on T such that vertical bar g vertical bar(p) is integrable with respect to sigma and L-p(partial derivative T) is the space of functions f defined on the boundary of T such that vertical bar f vertical bar(p) is integrable with respect to the representing measure of the harmonic function 1. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free