Embeddings of Function Spaces via the Caffarelli-Silvestre Extension, Capacities and Wolff potentials

Pengtao Li, Shaoguang Shi, Rui Hu +1

Let $P_{\alpha }f(x,t)$ be the Caffarelli-Silvestre extension of a smooth function $f(x):{\mathbb{R}}^n\to {\mathbb{R}}_{+}^{n+1}:={\mathbb{R}}^n\times (0,\infty ).$ The purpose of this…