Hardy inequalities for Landau Hamiltonian and for Baouendi-Grushin operator with Aharonov-Bohm type magnetic field. Part I

Ari Laptev ^[1] ; Michael Ruzhansky ^[1] ; Nurgissa Yessirkegenov ^[1]
1. [1] Imperial College London (Reino Unido)
Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 125, Nº 2, 2019, págs. 239-269
Idioma: inglés
DOI: 10.7146/math.scand.a-114892
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Resumen
- In this paper we prove the Hardy inequalities for the quadratic form of the Laplacian with the Landau Hamiltonian type magnetic field. Moreover, we obtain a Poincaré type inequality and inequalities with more general families of weights. Furthermore, we establish weighted Hardy inequalities for the quadratic form of the magnetic Baouendi-Grushin operator for the magnetic field of Aharonov-Bohm type. For these, we show refinements of the known Hardy inequalities for the Baouendi-Grushin operator involving radial derivatives in some of the variables. The corresponding uncertainty type principles are also obtained.