TY - JOUR

T1 - Sums of weighted differentiation composition operators from weighted Bergman spaces to weighted Zygmund and Bloch-type spaces

AU - Manhas, Jasbir S.

AU - Al Ghafri, Mohammed S.

N1 - Funding Information:
The authors would like to thank the anonymous referee for his careful reading of the manuscript and providing valuable suggestions which help in improving the original manuscript. J. S. Manhas is supported by SQU Grant no. IG/SCI/MATH/20/08.
Publisher Copyright:
© 2021, Tusi Mathematical Research Group (TMRG).

PY - 2021/7

Y1 - 2021/7

N2 - Let H(D) be the space of analytic functions on the unit disc D and let S(D) denote the set of all analytic self maps of the unit disc D. Let Ψ=(ψj)j=0k be such that ψj∈ H(D) and φ∈ S(D). To treat the Stević–Sharma type operators and the products of composition operators, multiplication operators, differentiation operators in a unified manner, Wang et al. considered the following sum operator: TΨ,φkf=∑j=0kψj·f(j)∘φ=∑j=0kDψj,φjf,f∈H(D).We characterize the boundedness and compactness of the operators TΨ,φk from the weighted Bergman spaces Av,p to the weighted Zygmund-type spaces Zw and the weighted Bloch-type spaces Bw. Besides, giving examples of bounded, unbounded, compact and non-compact operators TΨ,φk, we give an example of two unbounded weighted differentiation composition operators Dψ0,φ0,Dψ1,φ1:Av,p⟶Zw(Bw) such that their sum operator Dψ0,φ0+Dψ1,φ1=TΨ,φ1:Av,p⟶Zw(Bw) is bounded.

AB - Let H(D) be the space of analytic functions on the unit disc D and let S(D) denote the set of all analytic self maps of the unit disc D. Let Ψ=(ψj)j=0k be such that ψj∈ H(D) and φ∈ S(D). To treat the Stević–Sharma type operators and the products of composition operators, multiplication operators, differentiation operators in a unified manner, Wang et al. considered the following sum operator: TΨ,φkf=∑j=0kψj·f(j)∘φ=∑j=0kDψj,φjf,f∈H(D).We characterize the boundedness and compactness of the operators TΨ,φk from the weighted Bergman spaces Av,p to the weighted Zygmund-type spaces Zw and the weighted Bloch-type spaces Bw. Besides, giving examples of bounded, unbounded, compact and non-compact operators TΨ,φk, we give an example of two unbounded weighted differentiation composition operators Dψ0,φ0,Dψ1,φ1:Av,p⟶Zw(Bw) such that their sum operator Dψ0,φ0+Dψ1,φ1=TΨ,φ1:Av,p⟶Zw(Bw) is bounded.

KW - Bounded and compact operators

KW - Weighted Bergman spaces

KW - Weighted Bloch spaces

KW - Weighted composition operators

KW - Weighted differentiation composition operators

KW - Weighted Zygmund spaces

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U2 - 10.1007/s43036-021-00147-0

DO - 10.1007/s43036-021-00147-0

M3 - Article

AN - SCOPUS:85107032293

VL - 6

JO - Advances in Operator Theory

JF - Advances in Operator Theory

SN - 2538-225X

IS - 3

M1 - 51

ER -