In this work we will present a new characterization of the Sobolev space W^{1,1}(\R^n) and also we give another proof of the characterization of the Sobolev space W^{1,p}(\R^n), 1<p<\infty, in terms of Poincaré inequalities. ...

Newton-Sobolev spaces, as presented by N. Shanmugalingam, describe a way to extend Sobolev spaces to the metric setting via upper gradients, for metric spaces with ´sucient´ paths of nite length. Sometimes, as is the case ...

We study the embeddings of variable exponent Sobolev and Hölder function spaces over Euclidean domains, providing necessary and/or sufficient conditions on the regularity of the exponent and/or the domain in various contexts. ...

In this paper we define the fractional order Orlicz-Sobolev spaces, and prove its convergence to the classical Orlicz-Sobolev spaces when the fractional parameter s↑1 in the spirit of the celebrated result of Bourgain-Br ...

We define the notion of nonlocal magnetic Sobolev spaces with nonstandard growth for Lipschitz magnetic fields. In this context we prove a Bourgain-Brezis- Mironescu type formula for functions in this space as well as for ...

We obtain improved fractional Poincaré and Sobolev-Poincaré inequalities including powers of the distance to the boundary in bounded John, s-John, and Hölder-α domains, and discuss their optimality.

In this article we extend the Sobolev spaces with variable exponents to include the fractional case, and we prove a compact embedding theorem of these spaces into variable exponent Lebesgue spaces. As an application we ...

In this note we prove the validity of the Maz'ya-Shaposhnikova formula in magnetic fractional Orlicz-Sobolev spaces. This complements a previous asymptotic study of the limit as s ↑ 1 performed by the second author in ...