An application of atomic decomposition in Bergman spaces to the study of differences of composition operators

Abstract

In this paper we characterize bounded differences of composition operators from standard weighted Bergman spaces Aαp into Lebesgue spaces Lq(μ) when α>−1 and p>q. In the process we also find an interesting connection between the difference operator and certain weighted composition operators answering a question raised in Saukko (2011) [18]. By combining the results of this paper with those of Saukko (2011) [18], we obtain a complete characterization of bounded and compact differences between standard weighted Bergman spaces.