Sums of generalized weighted composition operators from weighted Bergman spaces to weighted Banach spaces

Mohammed Said Al Ghafri


The present research provides both necessary and sufficient conditions for the sum operator \mathcal{S}_{\mu,\eta}^k to exhibit boundedness and compactness when mapping from the weighted Bergman spaces \mathcal{A}_v^p to the weighted Banach spaces H_w^\infty(H_w^0). This unification encompasses the product of multiplication, differentiation, and composition operators. Furthermore, we provide an example to demonstrate that the boundedness of the operator \mathcal{S}_{\mu,\eta}^k:\mathcal{A}_v^p\longrightarrow H_w^\infty does not necessarily imply the boundedness of the operator \mathcal{S}_{\mu,\eta}^k:\mathcal{A}_v^p\longrightarrow H_w^0. Also, we present an example of a bounded operator \mathcal{S}_{\mu,\eta}^k:H_v^\infty\longrightarrow H_w^\infty, while the operator \mathcal{S}_{\mu,\eta}^k:\mathcal{A}_v^p\longrightarrow H_w^\infty is not bounded.


weighted Banach space; little weighted Banach space; weighted Bergman spaces; bounded operators; compact operators; generalized weighted composition operators

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Copyright (c) 2024 Mohammed Said Al Ghafri, Mohammed Said Al Ghafri

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Digital Object Identifier DOI: 10.21533/scjournal

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