Is the distribution $f\mapsto \int_{S} \frac{\partial^i }{\partial \nu^i}f\,\mathrm{dvol}$ in a Bessel potential space?

In order to finish a paper on ‘metric space magnitude’ I need to prove that a certain distribution on $\mathbb{R}^{2p+1}$ is in Mark Meckes’ weighting space (see Magnitude, Diversity, Capacities, and Dimensions of Metric Spaces). My question requires no knowledge of that background, however: for what I want to do, it suffices to show that … Read more

Fractional Sobolev spaces and interpolation in unbounded Lipschitz domains

I am not really familiar with the topic, thus I am looking for some references about the following problem. Let s>0 be a positive real and let p∈(1,+∞). We define the Bessel Potential spaces on Rn via the Fourier transform F as follows. Hs,p(Rn)={f∈Lp(Rn):F−1(1+|ξ|2)s2Ff∈Lp(Rn)}. In the case of s∈Z+ it holds that Hs,p(Rn)=Ws,p(Rn) where the … Read more