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

  • Ari Laptev
  • Michael Ruzhansky
  • Nurgissa Yessirkegenov

Abstract

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.

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Published
2019-10-19
How to Cite
Laptev, A., Ruzhansky, M., & Yessirkegenov, N. (2019). Hardy inequalities for Landau Hamiltonian and for Baouendi-Grushin operator with Aharonov-Bohm type magnetic field. Part I. MATHEMATICA SCANDINAVICA, 125(2), 239-269. https://doi.org/10.7146/math.scand.a-114892
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Articles