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Extension theorems of Whitney type by the use of integral operators by Gudayol, Jaume is a scholarly article available to read on EtoBox.

What is Extension theorems of Whitney type by the use of integral operators about?

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.

Author

Gudayol, Jaume

Published

1998

Language

EN