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arXiv · 2309.16113

Stevi\'c-Sharma type operators between Bergman spaces induced by doubling weights

Juntao Du·Songxiao Li·Zuoling Liu
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Abstract

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 Stevi\'c-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.

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Juntao Du, Songxiao Li, Zuoling Liu. 2023-09-28. Stevi\'c-Sharma type operators between Bergman spaces induced by doubling weights. https://arxiv.org/abs/2309.16113

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