Horizontal magnetic fields and improved Hardy inequalities in the Heisenberg group

Autor:	Cassano, Biagio, Franceschi, Valentina, Krejcirik, David, Prandi, Dario
Rok vydání:	2021
Předmět:	Mathematics - Spectral Theory Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	In this paper we introduce a notion of magnetic field in the Heisenberg group and we study its influence on spectral properties of the corresponding magnetic (sub-elliptic) Laplacian. We show that uniform magnetic fields uplift the bottom of the spectrum. For magnetic fields vanishing at infinity, including Aharonov--Bohm potentials, we derive magnetic improvements to a variety of Hardy-type inequalities for the Heisenberg sub-Laplacian. In particular, we establish a sub-Riemannian analogue of Laptev and Weidl sub-criticality result for magnetic Laplacians in the plane. Instrumental for our argument is the validity of a Hardy-type inequality for the Folland--Stein operator, that we prove in this paper and has an interest on its own. Comment: 44 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2110.13775 Zobrazit plný text záznamu View this record from Arxiv