We study the smoothing effect of averaging over spheres for solutions of kinetic transport equations in hyperbolic Sobolev spaces.

We establish a full range of Caffarelli-Kohn-Nirenberg inequalities and their variants for fractional Sobolev spaces.

We consider fractional Sobolev spaces with dominating mixed derivatives and prove generalizations of Trudinger’s limiting imbedding theorem.

In this article, we re-examine some of the classical pointwise multiplication theorems in Sobolev-Slobodeckij spaces, part motivated by a simple counter-example that illustrates how certain fail spaces when bounded domain is replaced Rn. We identify source failure, and examine why same failure not encountered Bessel potential spaces. To analyze situation, begin with survey results stated proved...