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

In this paper we characterize bounded differences of composition operators from standard weighted Bergman spaces A pα 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. © 2012 Elsevier Inc. All rights reserved