Weighted composition operators from the Besov spaces into the weighted-type space Hμ∞

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:402

Article

Colonna, Flavia¹  Tjani, Maria² 

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

[2] Univ Arkansas, Dept Math Sci, Fayetteville, AR 72701 USA

关键词: Weighted composition operator;    Besov space;    Dirichlet space;    Weighted-type space;    BMOA;    Hardy space;    Bloch space;   

DOI  :  10.1016/j.jmaa.2013.01.037

来源: Elsevier

【 摘 要 】

Let mu denote a positive continuous function on the open unit disk D. In this work, we characterize the bounded weighted composition operators from the analytic Besov spaces B-p (1 <= p < infinity) into the weighted-type space H-mu(infinity) consisting of the analytic functions on D such that sup(z is an element of D) mu(z)vertical bar f(z)vertical bar < infinity and determine their operator norms. We also determine the essential norm of the bounded weighted composition operators acting on the Dirichlet space and obtain explicit estimates when p = 1. In the general case when the operator maps B-p into H-mu(infinity), we derive an approximation of the essential norm that yields a characterization of the compact weighted composition operators. Finally, we derive characterizations of the bounded and the compact weighted composition operators from the spaces of antiderivatives of functions in B-p and BMOA into the alpha-Bloch spaces. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free