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

TL;DR

This paper estimates the norms of Stević-Sharma type operators between weighted Bergman spaces using advanced inequalities and atomic decompositions, removing previous restrictions and providing new interpolation results for these spaces.

Contribution

It introduces new norm estimates for operators between weighted Bergman spaces that eliminate earlier limitations and includes an interpolation theorem for spaces induced by doubling weights.

Findings

Norm and essential norm estimates for operators between weighted Bergman spaces.

Removal of restrictions present in previous results.

An interpolation theorem for Bergman spaces with doubling weights.

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.