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

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 $H^p(\mathbb{D})$, $1\le p\le \mathrm{\infty }$, and weighted Bergman spaces $A_{\beta }^p(\mathbb{D})$, $-1<\beta <\mathrm{\infty }$ and $1<p<\mathrm{\infty }$.