Extension theorems of Whitney type by the use of integral operators

Details Extension theorems of Whitney type by the use of integral operators Extension theorems of Whitney type by the use of integral operators

1998-03-05

arxiv.org/abs/math/9803016v2

Mathematics

Classical Analysis and ODEs

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

Scientific paper

Given 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.

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