Affiliation:
1. School of Computer Science, University of Electronic Science and Technology of China, Zhongshan Institute, Zhongshan 528402, China
2. School of Mathematical Sciences, Qufu Normal University, Qufu 273100, China
Abstract
The single generalized weighted composition operator Du,ψn on various spaces of analytic functions has been investigated for decades, i.e., Du,ψnf=u·(f(n)∘ψ), where f∈H(D). However, the study of the finite sum of generalized weighted composition operators with different orders, i.e., PU,ψkf=u0·f∘ψ+u1·f′∘ψ+⋯+uk·f(k)∘ψ, is far from complete. The boundedness, compactness and essential norm of sums of generalized weighted composition operators from weighted Bergman spaces with doubling weights into Bloch-type spaces are investigated. We show a rigidity property of PU,ψk. Specifically, the boundedness and compactness of the sum PU,ψk is equivalent to those of each Dun,ψn, 0≤n≤k.
Funder
Guangdong Basic and Applied Basic Research Foundation