Traces of weighted Sobolev spaces with Muckenhoupt weight. The case p=1. (November 2015) - Tyulenev, A.I.
Abstract: A complete description of traces on R n of functions from the weighted Sobolev space W 1 l ( R n + 1, γ ), l ∈ N, with weight γ ∈ A 1 loc ( R n + 1 ) is obtained. In the case l = 1 the proof of the trace theorem is based on a special nonlinear algorithm for constructing a system of tilings of the space R n . As the trace of the space W 1 1 ( R n + 1, γ ) we have the new function space Z ( γ k, m ) .