Some Operator Ideal Properties of Volterra Operators on Bergman and Bloch Spaces

We characterize the integration operators V g with symbol g for which V g acts as an absolutely summing operator on weighted Bloch spaces B β and on weighted Bergman spaces A α p . We show that V g is r -summing on A α p , 1 ≤ p < ∞ , if and only if g belongs to a suitable Besov space. We also sh...

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Published inIntegral equations and operator theory Vol. 96; no. 1; p. 1
Main Authors Jreis, Joelle, Lefèvre, Pascal
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2024
Springer Nature B.V
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ISSN0378-620X
1420-8989
DOI10.1007/s00020-023-02742-7

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Summary:We characterize the integration operators V g with symbol g for which V g acts as an absolutely summing operator on weighted Bloch spaces B β and on weighted Bergman spaces A α p . We show that V g is r -summing on A α p , 1 ≤ p < ∞ , if and only if g belongs to a suitable Besov space. We also show that there is no non trivial nuclear Volterra operators V g on Bloch spaces and on Bergman spaces.
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ISSN:0378-620X
1420-8989
DOI:10.1007/s00020-023-02742-7