# Trace and extension theorems relating Besov spaces to weighted averaged Sobolev spaces

@article{Barton2016TraceAE, title={Trace and extension theorems relating Besov spaces to weighted averaged Sobolev spaces}, author={Ariel Barton}, journal={arXiv: Functional Analysis}, year={2016} }

There are known trace and extension theorems relating functions in a weighted Sobolev space in a domain U to functions in a Besov space on the boundary bU. 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…

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