Sobolev Type Embeddings in the Limiting Case.
Our aim is to establish Sobolev type inequalities for fractional maximal functions and Riesz potentials in weighted Morrey spaces of variable exponent on the half space . We also obtain Sobolev type inequalities for a function on . As an application, we obtain Sobolev type inequality for double phase functionals with variable exponents , where and satisfy log-Hölder conditions, for , and is nonnegative and Hölder continuous of order .
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.