Embedding theorems and integration operators on Bergman spaces with rapidly decreasing weights |
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| Authors: | Jordi Pau,José Á ngel Pelá ez |
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| Affiliation: | a Departament de Matemàtica Aplicada i Analisi, Universitat de Barcelona, 08007 Barcelona, Spain
b Departamento de Análisis Matemático, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, Spain |
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| Abstract: | We completely describe those positive Borel measures μ in the unit disc D such that the Bergman space Ap(w)⊂Lq(μ), 0<p,q<∞, where w belongs to a large class W of rapidly decreasing weights which includes the exponential weights  , α>0, and some double exponential type weights.As an application of that result, we characterize the boundedness and the compactness of Tg:Ap(w)→Aq(w), 0<p,q<∞, w∈W, where Tg is the integration operator |
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| Keywords: | Integration operators Bergman spaces Carleson measures Schatten classes |
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