Extension theorems of Whitney type by the use of integral operators

Abstract

Given a compact of ${\mathbf{R}}^n$, there is always a doubling measure having it as its support. We use this fact to construct an integral operator that extends differentiable functions defined on any compact set of ${\mathbf{R}}^n$ to the whole of ${\mathbf{R}}^n$. This allows us both to give a new proof of Whitney's extension theorem and to extend it to Besov spaces defined on arbitrary compact sets of ${\mathbf{R}}^n$. We also modify this operator to obtain, under certain assumptions, holomorphic extensions.

LaTeX 2.09 file, 28 p (2nd version, slightly longer proofs to make it mor citable.)