Traces and fractional Sobolev extension domains with variable exponent

摘要

Assume that RN is a bounded domain of class C0;1 and denotedby Ws;q(:);p(:;:) ( ) the fractional Sobolev space with variable exponent.We show that is a Ws;q(:);p(:;:)??extension domain for s 2 (0; 1). Asan application, we study complemented subspaces in Ws;q(:);p(:;:) via thetrace operator.