TRACE AND EXTENSION THEOREMS RELATING BESOV SPACES TO WEIGHTED AVERAGED SOBOLEV SPACES

摘要

There are known trace and extension theorems relating functions in a weighted Sobolev space in a domain Omega to functions in a Besov space on the boundary partial derivative Omega We extend these theorems to the case where the Sobolev exponent p is less than one by modifying our Sobolev spaces to consider averages of functions in Whitney balls. Averaged Sobolev spaces are also of interest in the applications in the case where p 1, and so we also provide trace and extension results in that case. Finally, we provide some comparable results for Neumann traces and extensions.