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arXiv · 1109.2339

How to recognize polynomials in higher order Sobolev spaces

Bogdan Bojarski·Lizaveta Ihnatsyeva·Juha Kinnunen
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Abstract

This paper extends characterizations of Sobolev spaces by Bourgain, Br\'{e}zis, and Mironescu to the higher order case. As a byproduct, we obtain an integral condition for the Taylor remainder term, which implies that the function is a polynomial. Similar questions are also considered in the context of Whitney jets.

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Bogdan Bojarski, Lizaveta Ihnatsyeva, Juha Kinnunen. 2011-09-11. How to recognize polynomials in higher order Sobolev spaces. https://arxiv.org/abs/1109.2339

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