Boundedness and Compactness of Weighted Composition Operators from (<i>α</i>, <i>k</i>)-Bloch Spaces to <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="bold-script">A</mi></mrow></semantics></math></inline-formula>_{(<i>β</i>,<i>k</i>)} Spaces on Generalized Hua Domains of the Fourth Kind

Abstract

This paper addresses the weighted composition operators Cϕψ from the (α,k)-Bloch spaces to the A(β,k) spaces of bounded holomorphic functions on W, where W is a generalized Hua domain of the fourth kind. Additionally, we obtain some necessary and sufficient conditions for the boundedness and compactness of these operators.

Keywords

• generalized Hua domain of the fourth type
• (<i>α</i>, <i>k</i>)-Bloch space
• A _(β,k) space%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="inline-formula"> <mml:math id="mm443"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">A</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </named-content>_{(<i>β</i>,<i>k</i>)} space
• weighted composition operators
• boundedness and compactness