Stević-Sharma type operators between Bergman spaces induced by doubling weights

Using Khinchin's inequality, Ger\(\check{\mbox{s}}\)gorin's theorem and the atomic decomposition of Bergman spaces, we estimate the norm and essential norm of Stević-Sharma type operators from weighted Bergman spaces \(A_\omega^p\) to \(A_\mu^q\) and the sum of weighted differentiation com...

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Bibliographic Details
Published inarXiv.org
Main Authors Du, Juntao, Li, Songxiao, Liu, Zuoling
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 28.09.2023
Subjects
Interpolation
Operators
Theorems
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Summary:Using Khinchin's inequality, Ger\(\check{\mbox{s}}\)gorin's theorem and the atomic decomposition of Bergman spaces, we estimate the norm and essential norm of Stević-Sharma type operators from weighted Bergman spaces \(A_\omega^p\) to \(A_\mu^q\) and the sum of weighted differentiation composition operators with different symbols from weighted Bergman spaces \(A_\omega^p\) to \(H^\infty\).The estimates of those between Bergman spaces remove all the restrictions of a result in [Appl. Math. Comput.,{\bf 217}(2011),8115--8125]. As a by-product, we also get an interpolation theorem for Bergman spaces induced by doubling weights.
ISSN:2331-8422