2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76668Given a compact of ${\bf R}^n$, 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 ${\bf R}^n$ to the whole of ${\bf R}^n$. 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 ${\bf R}^n$. 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.)Classical Analysis and ODEsComplex Variables26B20 (Primary) 26B35, 32A40 (Secondary)text