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math.FA2021★ 1 cited
A Sharp Lieb-Thirring Inequality for Functional Difference Operators
Ari Laptev, Lukas Schimmer
We prove sharp Lieb-Thirring type inequalities for the eigenvalues of a class of one-dimensional functional difference operators associated to mirror curves. We furthermore prove t…
math.FA2017
Hardy inequalities for Landau Hamiltonian and for Baouendi-Grushin operator with Aharonov-Bohm type magnetic field. Part I
Ari Laptev, Michael Ruzhansky, Nurgissa Yessirkegenov
In this paper we prove the Hardy inequalities for the quadratic form of the Laplacian with the Landau Hamiltonian magnetic field. Moreover, we obtain Poincaré type inequality and i…
math.FA2006★ 1 cited
Hardy inequalities for simply connected planar domains
Ari Laptev, Alexander V. Sobolev
In 1986 A. Ancona showed, using the Koebe one-quarter Theorem, that for a simply-connected planar domain the constant in the Hardy inequality with the distance to the boundary is g…