Extension theorems of Whitney type by the use of integral operators

Jaume Gudayol

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arXiv · math/9803016

Extension theorems of Whitney type by the use of integral operators

Jaume Gudayol

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Abstract

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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Jaume Gudayol. 1998-04-23. Extension theorems of Whitney type by the use of integral operators. https://arxiv.org/abs/math/9803016

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