Sobolev Type Embeddings in the Limiting Case.
The paper deals with spaces of Sobolev type where s > 0, 0 < p ≤ ∞, and their relations to corresponding spaces of Besov type where s > 0, 0 < p ≤ ∞, 0 < q ≤ ∞, in terms of embedding and real interpolation.
In a recent work, E. Cinti and F. Otto established some new interpolation inequalities in the study of pattern formation, bounding the Lr(μ)-norm of a probability density with respect to the reference measure μ by its Sobolev norm and the Kantorovich-Wasserstein distance to μ. This article emphasizes this family of interpolation inequalities, called Sobolev-Kantorovich inequalities, which may be established in the rather large setting of non-negatively curved (weighted) Riemannian manifolds by means...
We define a Sobolev space by means of a generalized Poincaré inequality and relate it to a corresponding space based on upper gradients.
In this paper we obtain several classes of separated locally convex spaces which are M-spaces. We give also some results on compact convex sets and new characterization of weak compactness.