99 citations · 403 across the 43 of their papers we have counts for
55 papers
Hardy and Sobolev inequalities on antisymmetric functions
Thomas Hoffmann-Ostenhof, Ari Laptev, Il'ya Shcherbakov
We obtain sharp Hardy inequalities on antisymmetric functions where antisymmetry is understood for multi-dimensional particles. Partially it is an extension of the previously publi…
Magnetic Lieb--Thirring inequalities on the torus
Alexei Ilyin, Ari Laptev
In this paper we prove Lieb--Thirring inequalities for magnetic Schrödinger operators on the torus, where the constants in the inequalities depend on the magnetic flux.
Lieb--Thirring inequalities on manifolds with constant negative curvature
Alexei Ilyin, Ari Laptev, Timon Weinmann
In this short note we prove Lieb--Thirring inequalities on manifolds with negative constant curvature. The discrete spectrum appears below the continuous spectrum $(d-1)^2/4, \inft…
Weighted CLR type bounds in two dimensions
Rupert L. Frank, Ari Laptev, Larry Read
We derive weighted versions of the Cwikel-Lieb-Rozenblum inequality for the Schrödinger operator in two dimensions with a nontrivial Aharonov-Bohm magnetic field. Our bounds captur…
An improved one-dimensional Hardy inequality
Rupert L. Frank, Ari Laptev, Timo Weidl
We prove a one-dimensional Hardy inequality on the halfline with sharp constant, which improves the classical form of this inequality. As a consequence of this new inequality we ca…
Hardy inequalities for magnetic -Laplacians
Cristian Cazacu, David Krejcirik, Nguyen Lam +1
We establish improved Hardy inequalities for the magnetic -Laplacian due to adding nontrivial magnetic fields. We also prove that for Aharonov-Bohm magnetic fields the sharp con…