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 …

In this paper we focus our attention on the following nonlinear fractional Schrödinger
equation with magnetic field ε 2 s (− Δ) A/ε s u+ V (x) u= f (| u| 2) u in RN, where ε> 0 is a …

Using energy methods, we prove some power-law and exponential decay estimates for
classical and nonlocal evolutionary equations. The results obtained are framed into a …

Under certain restrictions on s, p, q, the Triebel-Lizorkin spaces can be viewed as
generalised fractional Sobolev spaces W qs, p. In this article, we show that the Bourgain …

FRACTIONAL LAPLACIANS, PERIMETERS AND HEAT SEMIGROUPS IN CARNOT GROUPS
Fausto Ferrari Michele Miranda Jr. Diego Pallara Andrea P Page 1 Manuscript submitted to …

Motivated by the recent characterization of Sobolev spaces due to Brezis–Van Schaftingen–
Yung we prove new weak-type inequalities for one parameter families of operators …

The aim of this note is to survey recent results contained in Nguyen HM, Squassina M.[On
anisotropic Sobolev spaces. Commun Contemp Math, to appear. DOI: 10.1142 …

We consider the following nonlinear fractional Choquard equation $$\varepsilon^{2s}(-
\Delta)^{s} _ {A/\varepsilon} u+ V (x) u=\varepsilon^{\mu-N}\left (\frac {1}{| x|^{\mu}}* F …

In this paper we present an interpolation approach to the fractional Sobolev spaces in
Carnot groups using the K-method. This approach provides us with a different …

This paper is concerned with the multiplicity and concentration behavior of nontrivial
solutions for the following fractional Kirchhoff equation in presence of a magnetic field:\begin …