Composition Operators and Rational Inner Functions II: Boundedness between two different Bergman Spaces

Abstract

In this note we provide a sufficient condition on when the composition operator $C_{\hat{I}}¦:A_a^2({\mathbb{D}}^2)\to A_{\hat{I}}^2({\mathbb{D}}^2)$ is bounded, whenever $a\ge -1$ and ${\hat{I}}^2$ is positive, with the assumption that $\hat{I}¦$ is induced by non-smooth Rational Inner Functions.

5 pages, comments are welcome!