Extension theorems of Whitney type by the use of integral operators

1998/03/05 by Jaume Gudayol, Gudayol, Jaume
Mathematics · #26B20 (Primary) 26B35 #32A40 (Secondary) #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods #math.CA #math.CV #msc:26B20 #msc:26B35 #msc:32A40

paper · pdf · doi:10.48550/arxiv.math/9803016

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

openalex publication_date 1998/03/05 · arxiv created 1998/04/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a compact of \bf Rⁿ, 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 Rⁿ to the whole of \bf Rⁿ. 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 Rⁿ. We also modify this operator to obtain, under certain assumptions, holomorphic extensions.

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