On the Trace of $W_{a}^{m+1,1}(\mathbb{R}_{+}^{n+1})$

Giovanni Leoni, Daniel Spector

Published 2024-04-29Version 1

In this paper, we give a simple proof that any function in the Besov space $B^{m-a,1}(\mathbb{R}^{n})$ can be extended to a function in $W_{a}^{m+1,1}(\mathbb{R}_{+}^{n+1})$. In particular, utilizing the intrinsic seminorm in $B^{m-a,1}(\mathbb{R}^{n})$, we show that either a suitably scaled heat extension or the harmonic extension provides one with the desired lifting.