Reduced Sobolev Inequalities

Abstract

AbstractThe Sobolev inequality of ordermasserts that ifp≧ 1,mp<nand1/q = 1/p — m/n,then the Lq-norm of a smooth function with compact support in Rnis bounded by a constant times the sum of theLp-norms of the partial derivatives of ordermof that function. In this paper we show that that sum may be reduced to include only the completely mixed partial derivatives or orderm,and in some circumstances even fewer partial derivatives.