On the Maz'ya-Shaposhnikova formula in Orlicz-Sobolev spaces on Carnot groups

TL;DR

This paper investigates the behavior of fractional Orlicz-Sobolev seminorms as the fractional parameter approaches zero within Carnot groups, extending previous research in this area.

Contribution

It provides new insights into the limit behavior of fractional Orlicz-Sobolev seminorms on Carnot groups, completing earlier partial studies.

Findings

Established the limit of fractional Orlicz-Sobolev seminorms as s approaches zero

Extended the Maz'ya-Shaposhnikova formula to Carnot groups in the Orlicz setting

Closed the gap in the previous study on this topic

Abstract

In this note we study the limit as $s\downarrow 0$ of fractional Orlicz-Sobolev seminorms in Carnot groups. This closes the study started in [10]