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 - Funding Information:
The second author is supported by SQU Grant No. IG/SCI/MATH/20/08.
Publisher Copyright:
© 2022 World Scientific Publishing Company.

PY - 2022/11/1

Y1 - 2022/11/1

N2 - Let H(D) be the space of analytic functions on the unit disc and let (D) denote the set of analytic self-maps of D. Let Ψ = (ψj)j=0k be such that ψj ∈ H(D) and φ ∈ S(D). We characterize the boundedness, compactness and completely continuous of the sum of generalized weighted composition operators 'Equation Presented' between weighted Banach spaces of analytic functions Hv∞(Hv0) and Hw∞(Hw0) 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 Dψ,φn: v(ßv0) → w(ßw0), v(ßv0) → Hw∞(Hw0) and Hv∞(Hv0) → w(ßw0), where v(ßv0) and w(ßw0) are weighted Bloch-type (little Bloch-type) spaces. Also, new characterizations of the boundedness and compactness of the operators TΨ,φk and DΨ,φn are given. Examples of bounded, unbounded, compact and non-compact operators TΨ,φk and DΨ,φn are given to explain the role of inducing functions Ψj, φ and the weights v, w of the underlying weighted spaces.

AB - Let H(D) be the space of analytic functions on the unit disc and let (D) denote the set of analytic self-maps of D. Let Ψ = (ψj)j=0k be such that ψj ∈ H(D) and φ ∈ S(D). We characterize the boundedness, compactness and completely continuous of the sum of generalized weighted composition operators 'Equation Presented' between weighted Banach spaces of analytic functions Hv∞(Hv0) and Hw∞(Hw0) 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 Dψ,φn: v(ßv0) → w(ßw0), v(ßv0) → Hw∞(Hw0) and Hv∞(Hv0) → w(ßw0), where v(ßv0) and w(ßw0) are weighted Bloch-type (little Bloch-type) spaces. Also, new characterizations of the boundedness and compactness of the operators TΨ,φk and DΨ,φn are given. Examples of bounded, unbounded, compact and non-compact operators TΨ,φk and DΨ,φn are given to explain the role of inducing functions Ψj, φ and the weights v, w of the underlying weighted spaces.

KW - Composition operators

KW - bounded and compact 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

SN - 1793-5571

VL - 15

JO - Asian-European Journal of Mathematics

JF - Asian-European Journal of Mathematics

IS - 11

M1 - 2250192

ER -