English

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.

Keywords

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}
}
R2 v1 2026-06-21T19:03:13.057Z