Horizontal magnetic fields and improved Hardy inequalities in the Heisenberg group
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F23%3A00373043" target="_blank" >RIV/68407700:21340/23:00373043 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1080/03605302.2023.2191326" target="_blank" >https://doi.org/10.1080/03605302.2023.2191326</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/03605302.2023.2191326" target="_blank" >10.1080/03605302.2023.2191326</a>
Alternative languages
Result language
angličtina
Original language name
Horizontal magnetic fields and improved Hardy inequalities in the Heisenberg group
Original language description
In this article, 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 article and has an interest on its own.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GX20-17749X" target="_blank" >GX20-17749X: New challenges for spectral theory: geometry, advanced materials and complex fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Communications in Partial Differential Equations
ISSN
0360-5302
e-ISSN
1532-4133
Volume of the periodical
48
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
42
Pages from-to
711-752
UT code for WoS article
000986352200001
EID of the result in the Scopus database
2-s2.0-85159042826