Sharp bounds for composition with quasiconformal mappings in Sobolev spaces

Marcos Oliva, Martí Prats

Let $\varphi$ be a quasiconformal mapping, and let $T_{\varphi }$ be the composition operator which maps $f$ to $f\circ \varphi$. Since $\varphi$ may not be bi-Lipschitz, the composition operator need not map…