@article{Laptev_Ruzhansky_Yessirkegenov_2019, title={Hardy inequalities for Landau Hamiltonian and for Baouendi-Grushin operator with Aharonov-Bohm type magnetic field. Part I}, volume={125}, url={https://www.mscand.dk/article/view/114892}, DOI={10.7146/math.scand.a-114892}, abstractNote={<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 PoincarĂ© 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>}, number={2}, journal={MATHEMATICA SCANDINAVICA}, author={Laptev, Ari and Ruzhansky, Michael and Yessirkegenov, Nurgissa}, year={2019}, month={Oct.}, pages={239â€“269} }