How to Recognize Polynomials in Higher Order Sobolev Spaces
AbstractThis 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.
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