TY - JOUR AU - Laptev, Ari AU - Ruzhansky, Michael AU - Yessirkegenov, Nurgissa PY - 2019/10/19 Y2 - 2024/03/28 TI - Hardy inequalities for Landau Hamiltonian and for Baouendi-Grushin operator with Aharonov-Bohm type magnetic field. Part I JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 125 IS - 2 SE - Articles DO - 10.7146/math.scand.a-114892 UR - https://www.mscand.dk/article/view/114892 SP - 239-269 AB - <p>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.</p> ER -