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How to Recognize Polynomials in Higher Order Sobolev Spaces

Bogdan Bojarski, Lizaveta Ihnatsyeva, JUHA KINNUNEN JUHA KINNUNEN

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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DOI: http://dx.doi.org/10.7146/math.scand.a-15239

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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