Asymptotic behaviours in Fractional Orlicz-Sobolev spaces on Carnot groups

TL;DR

This paper introduces fractional Orlicz-Sobolev spaces on Carnot groups and investigates their asymptotic behavior as the fractional parameter approaches 0 and 1, extending classical results to a non-Euclidean setting.

Contribution

It defines new fractional Orlicz-Sobolev spaces on Carnot groups and analyzes their asymptotic properties, generalizing known Euclidean results to sub-Riemannian geometries.

Findings

Asymptotic behavior of Orlicz functionals as fractional parameter approaches 1

Asymptotic behavior of Orlicz functionals as fractional parameter approaches 0

Extension of classical results to Carnot group setting

Abstract

In this article we define a class of fractional Orlicz-Sobolev spaces on Carnot groups and, in the spirit of the celebrated results of Bourgain-Brezis-Mironescu and of Maz'ya-Shaposhnikova, we study the asymptotic behavior of the Orlicz functionals when the fractional parameter goes to $1$ and $0$.