How to recognize polynomials in higher order Sobolev spaces
Classical Analysis and ODEs
2011-09-13 v1
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.
Cite
@article{arxiv.1109.2339,
title = {How to recognize polynomials in higher order Sobolev spaces},
author = {Bogdan Bojarski and Lizaveta Ihnatsyeva and Juha Kinnunen},
journal= {arXiv preprint arXiv:1109.2339},
year = {2011}
}