Our concern in this paper lies with two aspects of weighted exponential spaces connected with their role of target spaces for critical imbeddings of Sobolev spaces. We characterize weights which do not change an exponential space up to equivalence of norms. Specifically, we first prove that Lexp tα(χB) = Lexp tα(ρ) if and only if ρq ∈ Lq with some q > 1. Second, we consider the Sobolev space W ...

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.