Methods and Applications of Analysis

Volume 21 (2014)

Number 4

Special issue dedicated to the 60th birthday of Stephen S.-T. Yau: Part II

Guest editors: John Erik Fornæss, Xiaojun Huang, Song-Ying Li, Yat Sun Poon, Wing Shing Wong, and Zhouping Xin

A representation theorem and its applications to characterize bounded and compact composition operators on Besov spaces on domains in $\mathbb{C}^N$

Pages: 407 – 426

DOI: https://dx.doi.org/10.4310/MAA.2014.v21.n4.a1

Authors

Hyungwoon Koo (Department of Mathematics, Korea University, Seoul, Korea)

Song-Ying Li (Department of Mathematics, University of California at Irvine)

Sujuan Long (School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian, China)

Abstract

We prove a representation theorem for Besov space on smooth bounded strictly pseudoconvex domain. As applications we characterize the boundedness and the compactness of composition operators on Besov spaces.

Keywords

representation theorem, composition operator, Besov space, strictly pseudoconvex domain

2010 Mathematics Subject Classification

Primary 32A10. Secondary 47B33.

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Published 9 October 2014