arXiv subjects
Publications and source records attributed to Zuoling Liu.
Based on a judicious partitioning of the preimage of the pseudohyperbolic disk under the composition symbols, in this article, we show that the boundedness and compactness of the sum of two generalized weighted composition operators with different symbols and orders between Bergman spaces are properly determined by each of individual summands.
Using some estimates in [J. Funct. Anal. {\bf 278}(2020), Article No. 108401], we completely characterized the boundedness and compactness of the Stevi\'c-Sharma type operators with different weights and different composition symbols between Bergman spaces induced by two-sides 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 $A_ω^p$ to $A_μ^q$ and the sum of weighted differentiation composition operators with different symbols from weighted Bergman spaces $A_ω^p$ 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.
In this paper, the order boundedness and essential norm of generalized weighted composition operators on Bergman spaces with doubling weights are characterized. Specially, we estimate the essential norm of these operators on weighted Bergman spaces by using the reduce order method.