Wavelet and Linear Algebra

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.