TY - JOUR
T1 - Sum of generalized weighted composition operators between weighted spaces of analytic functions
AU - Al Ghafri, Mohammed Said
AU - Manhas, Jasbir Singh
N1 - Publisher Copyright:
© 2022 World Scientific Publishing Company.
PY - 2022
Y1 - 2022
N2 - Let be the space of analytic functions on the unit disc and let denote the set of analytic self-maps of . Let ψ = (ψj)j=0k be such that ψj and φ . We characterize the boundedness, compactness and completely continuous of the sum of generalized weighted composition operators Tψ,φkf =Ζ j=0kψ j ⋅ f(j) φ =Ζ j=0k ψj,φjf,f , between weighted Banach spaces of analytic functions Hv∞(H v0) and Hw∞(H w0) which unifies the study of products of composition operators, multiplication operators and differentiation operators. As applications, we obtain the boundedness and compactness of the generalized weighted composition operators ψ,φn:Ζ v(Ζv0) →Ζ w(Ζw0), Ζv(Ζv0) → H w∞(H w0) and Hv∞(H v0) →Ζ w(Ζw0), where Ζv(Ζv0) and Ζw(Ζw0) are weighted Bloch-type (little Bloch-type) spaces. Also, new characterizations of the boundedness and compactness of the operators Tψ,φk and ψ,φn are given. Examples of bounded, unbounded, compact and non-compact operators Tψ,φk and ψ,φn are given to explain the role of inducing functions ψj, φ and the weights v, w of the underlying weighted spaces.
AB - Let be the space of analytic functions on the unit disc and let denote the set of analytic self-maps of . Let ψ = (ψj)j=0k be such that ψj and φ . We characterize the boundedness, compactness and completely continuous of the sum of generalized weighted composition operators Tψ,φkf =Ζ j=0kψ j ⋅ f(j) φ =Ζ j=0k ψj,φjf,f , between weighted Banach spaces of analytic functions Hv∞(H v0) and Hw∞(H w0) which unifies the study of products of composition operators, multiplication operators and differentiation operators. As applications, we obtain the boundedness and compactness of the generalized weighted composition operators ψ,φn:Ζ v(Ζv0) →Ζ w(Ζw0), Ζv(Ζv0) → H w∞(H w0) and Hv∞(H v0) →Ζ w(Ζw0), where Ζv(Ζv0) and Ζw(Ζw0) are weighted Bloch-type (little Bloch-type) spaces. Also, new characterizations of the boundedness and compactness of the operators Tψ,φk and ψ,φn are given. Examples of bounded, unbounded, compact and non-compact operators Tψ,φk and ψ,φn are given to explain the role of inducing functions ψj, φ and the weights v, w of the underlying weighted spaces.
KW - bounded and compact operators
KW - Composition operators
KW - generalized weighted composition operators
KW - multiplication operators
KW - weighted Banach spaces
KW - weighted Bloch-type spaces
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U2 - 10.1142/S1793557122501923
DO - 10.1142/S1793557122501923
M3 - Article
AN - SCOPUS:85125742906
JO - Asian-European Journal of Mathematics
JF - Asian-European Journal of Mathematics
SN - 1793-5571
ER -