Related papers: Quantitative Hardy inequality for magnetic Hamilto…
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type inequality that takes…
In this paper we prove the Hardy inequalities for the quadratic form of the Laplacian with the Landau Hamiltonian magnetic field. Moreover, we obtain Poincar\'e type inequality and inequalities with more general families of weights, all…
We establish Lieb-Thirring type inequalities for non self-adjoint relatively compact perturbations of certain operators of mathematical physics. We apply our results to quantum Hamiltonians of Schr{\"o}dinger and Pauli with constant…
The main results of this paper concern sharp constant of the Trudinger-Moser inequality in $\mathbb{R}^{2}$ for Aharonov-Bohm magnetic fields. This is a borderline case of the Hardy type inequalities for Aharonov-Bohm magnetic fields in…
We establish improved Hardy inequalities for the magnetic $p$-Laplacian due to adding nontrivial magnetic fields. We also prove that for Aharonov-Bohm magnetic fields the sharp constant in the Hardy inequality becomes strictly larger than…
We deal with Dirac operators with external homogeneous magnetic fields. Hardy-type inequalities related to these operators are investigated: for a suitable class of transversal magnetic fields, we prove a Hardy inequality with the same best…
We study functional and spectral properties of perturbations of the magnetic Laplace operator on the circle. This operator appears when considering the restriction to the unit circle of a two-dimensional Schr{\"o}dinger operator with the…
We proved some optimal Hardy inequalities in RNwhich is closely related to multipolar Schr\"odinger operators with mean-value type potentials, these sharp inequalities imply some multipolar type Heisenberg inequalities. We also obtained…
We show that allowing magnetic fields to be complex-valued leads to an improvement in the magnetic Hardy-type inequality due to Laptev and Weidl. The proof is based on the study of momenta on the circle with complex magnetic fields, which…
In this paper we introduce a notion of magnetic field in the Heisenberg group and we study its influence on spectral properties of the corresponding magnetic (sub-elliptic) Laplacian. We show that uniform magnetic fields uplift the bottom…
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 can rederive known doubly weighted Hardy inequalities. Our…
In this paper we obtain quite general and definitive forms for Hardy-Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simpler and straightforward proofs and we are able to…
This paper is devoted to a collection of results on nonlinear interpolation inequalities associated with Schr{\"o}dinger operators involving Aharonov-Bohm magnetic potentials, and to some consequences. As symmetry plays an important role…
We give a short and unified proof of Hardy-Lieb-Thirring inequalities for moments of eigenvalues of fractional Schroedinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, Soerensen,…
We study the quadratic form associated to the kinetic energy operator in the presence of an external magnetic field in d = 3. We show that if the radial component of the magnetic field does not vanish identically, then the classical lower…
We prove that the number of negative eigenvalues of two-dimensional magnetic Schroedinger operators is bounded from above by the strength of the corresponding electric potential. Such estimates fail in the absence of a magnetic field. We…
We derive Hardy type inequalities for a large class of sub-elliptic operators that belong to the class of $\Delta_\lambda$-Laplacians and find explicit values for the constants involved. Our results generalize previous inequalities obtained…
In this paper we establish a Hardy inequality for Laplace operators with Robin boundary conditions. For convex domains, in particular, we show explicitly how the corresponding Hardy weight depends on the coefficient of the Robin boundary…
We provide lower bounds for the sum of the negative eigenvalues of the operator $|\sigma\cdot p_A|^{2s} - C_s/|x|^{2s} + V$ in three dimensions, where $s\in (0, 1]$, covering the interesting physical cases $s = 1$ and $s = 1/2$. Here…
We study a two-dimensional Pauli operator describing a charged quantum particle with spin $1/2$ moving on a plane in presence of an orthogonal Aharonov-Bohm magnetic flux. We classify all the admissible self-adjont realizations and give a…