TY - JOUR
AU - Laptev, Ari
AU - Ruzhansky, Michael
AU - Yessirkegenov, Nurgissa
PY - 2019/10/19
Y2 - 2023/09/26
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 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>
ER -