How to Recognize Polynomials in Higher Order Sobolev Spaces

Bogdan Bojarski; Lizaveta Ihnatsyeva; JUHA KINNUNEN JUHA KINNUNEN

doi:10.7146/math.scand.a-15239

How to Recognize Polynomials in Higher Order Sobolev Spaces

Authors

Bogdan Bojarski
Lizaveta Ihnatsyeva
JUHA KINNUNEN JUHA KINNUNEN

DOI:

https://doi.org/10.7146/math.scand.a-15239

Abstract

This paper extends characterizations of Sobolev spaces by Bourgain, Brézis, 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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Published

2013-06-01

How to Cite

Bojarski, B., Ihnatsyeva, L., & JUHA KINNUNEN, J. K. (2013). How to Recognize Polynomials in Higher Order Sobolev Spaces. MATHEMATICA SCANDINAVICA, 112(2), 161–181. https://doi.org/10.7146/math.scand.a-15239