Cong-Ming Li

$L^p$ isomorphisms for the fractional Laplacian on $\mathbb{R}^n$ and their application

A classical theory of Amrouche, Girault and Giroire (1994) resolves the Laplace equation on $\mathbb{R}^n$ through an isomorphism between weighted Sobolev spaces. Inspired by their framework, we develop the corresponding $L^p$ theory for the fractional Laplacian: we introduce weighted fractional Sobolev spaces $\Lambda...