The $s$-polyharmonic extension problem and higher-order fractional Laplacians

Abstract

We provide a detailed description of the relationships between the fractional Laplacian of order $2s\in (0,n)$ on ${\mathbb{R}}^n$ and the $\textit{$s$-polyharmonic}$ extension operator to the upper half space ${\mathbb{R}}_{+}^{n+1}$.

32 pages