Li-Yorke chaotic weighted composition operators on Hardy and Bergman spaces over the unit disk

Abstract

We study Li--Yorke and mean Li--Yorke chaos for weighted composition operators $C_{w,\phi }$ on Banach spaces of analytic functions on the unit disk $\mathbb{D}$. Under natural conditions on the space, we show that $C_{w,\phi }$ is (densely) Li--Yorke chaotic if and only if it is not power-bounded, and (densely) mean Li--Yorke chaotic if and only if it is not absolutely Cesàro bounded. These results are applied to Hardy spaces $H^p(\mathbb{D})$, $1\le p\le \infty$, and weighted Bergman spaces $A_{\beta }^p(\mathbb{D})$, $-1<\beta <\infty$ and $1<p<\infty$.

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