On the Whitney Problem for Weighted Sobolev Spaces

Given a closed weakly regular d-thick subset S of R-n, we prove the existence of a bounded linear extension operator Ext: Tr vertical bar SWp1 (R-n, gamma) -> W-p(1)(R-n, gamma) for p is an element of (1, infinity), 0 <= d <= n, is an element of (max{1, n - d}, p), l is an element of N, and gamma is an element of A(p/r)(R-n). In particular, we prove that a linear bounded trace space exists in the case where S is the closure of an arbitrary domain in R-n, gamma equivalent to 1, and p > n - 1. The obtained results supplement those of previous studies, in which a similar problem was considered either in the case of p is an element of (n, infinity) without constraints on the set S or in the case of p is an element of (1, infinity) under stronger constraints on the set S.