The Maz'ya-Shaposhnikova limit in the magnetic setting

TL;DR

This paper establishes a magnetic analogue of the Maz'ya-Shaposhnikova limit, extending the understanding of nonlocal norms in magnetic settings as the fractional parameter tends to zero.

Contribution

It introduces a magnetic version of the Maz'ya-Shaposhnikova limit, complementing previous results for the case when the parameter approaches one.

Findings

Proves a magnetic version of the Maz'ya-Shaposhnikova limit.

Complements existing convergence results for fractional parameters approaching one.

Enhances the theoretical framework for nonlocal norms in magnetic contexts.

Abstract

We prove a magnetic version of the Maz'ya-Shaposhnikova singular limit of nonlocal norms with vanishing fractional parameter. This complements a general convergence result recently obtained by authors when the parameter approaches one.