Related papers: Lieb-Thirring inequalities and other functional in…
In this paper we obtain sharp Lieb-Thirring inequalities for a Schr\"odinger operator on semi-axis with a matrix potential and show how they can be used to other related problems. Among them are spectral inequalities on star graphs and…
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 that the bottom of the essential spectrum of these operators…
We study in this article a new pointwise estimate for ''rough'' singular integral operators. From this pointwise estimate we will derive Sobolev type inequalities in a variety of functional spaces.
In this short article we show a particular version of the Hedberg inequality which can be used to derive, in a very simple manner, functional inequalities involving Sobolev and Besov spaces in the general setting of Lebesgue spaces of…
This paper considers Lieb-Thirring inequalities for higher order differential operators. A result for general fourth-order operators on the half-line is developed, and the trace inequality tr((-Delta)^2 - C^{HR}_{d,2} / (|x|^4) -…
In this paper, the versions of trigonometric functions of certain known inequalities for hyperbolic ones are proved, and then corresponding inequalities for means are presented.
In this paper, we investigate the convergence properties of Fourier partial sums associated with general orthonormal systems, focusing on functions that belong to specific differentiable function classes. While classical Fourier analysis…
Various miscellaneous functional inequalities are deduced for the so-called generalized inverse trigonometric and hyperbolic functions. For instance, functional inequalities for sums, difference and quotient of generalized inverse…
In a recent work of the author, a parabolic extension of the elliptic Ogawa type inequality has been established. This inequality is originated from the Brezis-Gallouet-Wainger logarithmic type inequalities revealing Sobolev embeddings in…
First and second-order inequalities of Friedrichs type for Sobolev functions in arbitrary domains are offered. The relevant inequalities involve optimal norms and constants that are independent of the geometry of the domain. Parallel…
In this paper we propose a novel family of weighted orthonormal rational functions on a semi-infinite interval. We write a sequence of integer-coefficient polynomials in several forms and derive their corresponding differential equations.…
Inequalities are established for certain trilinear scalar-valued functionals. These functionals act on measurable functions of one real variable, are defined by integration over two- or three-dimensional spaces, and are controlled in terms…
We prove a bound on the sum of the product of curl-free and divergence-free vector fields. Under appropriate orthonormality conditions our bound scales sublinearly in the number of terms, similar in spirit to Lieb--Thirring inequalities.
This paper is devoted to optimal functional inequalities for fractional Laplace operators on the sphere. Based on spectral properties, subcritical inequalities are established. Their consequences for fractional heat flows are considered.…
A logarithmic type Lieb-Thirring inequality for two-dimensional Schroedinger operators is established. The result is applied to prove spectral estimates on trapped modes in quantum layers.
We prove on the 2D sphere and on the 2D torus the Lieb-Thirring inequalities with improved constants for orthonormal families of scalar and vector functions.
This is a continuation of our previous work 0712.4092. It is well known that various isoperimetric inequalities imply their functional ``counterparts'', but in general this is not an equivalence. We show that under certain convexity…
We prove optimal Lieb-Thirring type inequalities for Schr\"odinger and Jacobi operators with complex potentials. Our results bound eigenvalue power sums (Riesz means) by the $L^p$ norm of the potential, where in contrast to the self-adjoint…
In this paper we obtain some operator versions of Levin-Steckin integral inequality.
We prove analogues of the Lieb-Thirring and Hardy-Lieb-Thirring inequalities for many-body quantum systems with fractional kinetic operators and homogeneous interaction potentials, where no anti-symmetry on the wave functions is assumed.…