Notes on the Sobolev (Semi)Norms of Quadratic Functions

Abstract

This paper studies the $H^0$ norm and $H^1$ seminorm of quadratic functions. The (semi)norms are expressed explicitly in terms of the coefficients of the quadratic function under consideration when the underlying domain is an $l_p$-ball (1 \leq p \leq \infty) in $R^n$ .