How to Recognize Polynomials in Higher Order Sobolev Spaces

• Autores: Bogdan Bojarski, Lizaveta Ihnatsyeva, Juha Kinnunen
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 112, Nº 2, 2013, págs. 161-181
• Idioma: inglés
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• Resumen

  • 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.