Littlewood Subordination Theorem and Composition Operators on Function Spaces with Variable Exponents

Document Type : Research Paper

Authors

1 Department of Mathemathics, Faculty of Science, Payame Noor University (PNU), P. O. Box 19395-4697, Tehran , Iran.

2 Department of Pure Mathemathics, Faculty of Science, Imam Khomeini International University, Qazvin 34149, Iran.

10.22072/wala.2023.1986385.1406

Abstract

This study concerns a detailed analysis of composition operators $C_\varphi$ on the classical Bergman spaces, as well as on the Hardy and Bergman spaces with variable exponents. Here, $\varphi$ is an analytic self-map of the open unit disk in the complex plane.
Accordingly, conditions for the boundedness of these operators are obtained. It is worth mentioning that the Littlewood subordination theorem plays a fundamental role in proving the stated theorems in which we use the Rubio de Francia extrapolation theorem.

Keywords


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