Related papers: Weighted CLR type bounds in two dimensions
In this work we obtain weighted boundedness results for singular integral operators with kernels exhibiting exponential decay. We also show that the classes of weights are characterized by a suitable maximal operator. Additionally, we study…
We estimate the rate of convergence, in the so-called large coupling limit, for Schr\"odinger type operators on bounded domains. The Schr\"odinger we deal with have "interaction potentials" supported in a compact inclusion. We show that if…
We consider Schroedinger operators on regular metric trees and prove Lieb-Thirring and Cwikel-Lieb-Rozenblum inequalities for their negative eigenvalues. The validity of these inequalities depends on the volume growth of the tree. We show…
This paper is devoted to the symmetry and symmetry breaking properties of a two-dimensional magnetic Schr{\"o}dinger operator involving an Aharonov-Bohm magnetic vector potential. We investigate the symmetry properties of the optimal…
We prove a variant of the so-called bilinear embedding theorem for operators in divergence form with complex coefficients and with nonnegative locally integrable potentials, subject to mixed boundary conditions, and acting on arbitrary open…
We analyze the Schr\"odinger operator in two-dimensions with an attractive potential given by a Bessel-Macdonald function. This operator is derived in the non-relativistic approximation of planar quantum electrodynamics (${\rm QED}_3$)…
In this paper, we show a weighted Hardy inequality in a limiting case for functions in weighted Sobolev spaces with respect to an invariant measure. We also prove that the constant in the left-hand side of the inequality is optimal. As…
We obtain bounds on the complex eigenvalues of non-self-adjoint Schr\"odinger operators with complex potentials, and also on the complex resonances of self-adjoint Schr\"odinger operators. Our bounds are compared with numerical results, and…
In this work we obtain boundedness results for fractional operators associated with Schr\"odinger operators $\ \mathcal{L}=-\Delta+V$ on weighted variable Lebesgue spaces. These operators include fractional integrals and their respective…
The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare obtained for both the fractional integral operators and the…
We prove upper and lower bounds for the number of eigenvalues of semi-bounded Schr\"odinger operators in all spatial dimensions. As a corollary, we obtain two-sided estimates for the sum of the negative eigenvalues of atomic Hamiltonians…
By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schroedinger operator possesses no point spectrum. The settings…
In this paper, we prove some equivalent characterizations of weighted Korenblum spaces and Bloch spaces in terms of symbols of bounded Hankel operators.
Using the technique of Gabor analysis, an equivalent characterization is established for the boundedness $e^{i\Delta}: W^{p,q}_m\rightarrow W^{p,q}$, where $0<p_i,q_i\leq\infty$ and $m$ is a $v$-moderate weight. The sharp exponents for the…
We provide a leading order semiclassical asymptotics of the energy of bound states for magnetic Neumann Schr\"odinger operators in two dimensional (exterior) domains with smooth boundaries. The asymptotics is valid all the way up to the…
Let $L=-\Delta+V$ be a Schr\"{o}dinger operator, where $\Delta $ is the Laplacian operator on $\rz$, while nonnegative potential $V$ belongs to the reverse H\"{o}lder class. In this paper, we establish the weighted norm inequalities for…
We consider the cubic nonlinear Schr\"odinger (NLS) equation set on a two dimensional box of size $L$ with periodic boundary conditions. By taking the large box limit $L \to \infty$ in the weakly nonlinear regime (characterized by smallness…
This paper is devoted to the study of the two-dimensional Dirac-Coulomb operator in presence of an Aharonov-Bohm external magnetic potential. We characterize the highest intensity of the magnetic field for which a two-dimensional magnetic…
We prove a weighted Carleman estimate for a class of one-dimensional, self-adjoint Schr\"odinger operators $P(h)$ with low regularity electric and magnetic potentials, where $h > 0$ is a semiclassical parameter. The long range part of…
In this paper, we investigate the weighted multilinear boundedness properties of the maximal higher order Calder\'on commutator for the dimensions larger than two. We establish all weighted multilinear estimates on the product of the…