Traces of weighted Sobolev spaces with Muckenhoupt weight. The case p=1p=1

A complete description of traces on RnRn of functions from the weighted Sobolev space W1l(Rn+1,γ), l∈Nl∈N, with weight γ∈A1loc(Rn+1) is obtained. In the case l=1l=1 the proof of the trace theorem is based on a special nonlinear algorithm for constructing a system of tilings of the space  RnRn. As the trace of the space W11(Rn+1,γ) we have the new function space Z({γk,m})Z({γk,m}).