相关论文: On certain generalized Hardy's inequalities and ap…
We undertake an analysis of Fredholm determinants arising from kernels whose defining functions satisfy a Schr\"odinger type equation. When this defining function is the Airy one, the evaluation of the corresponding Fredholm determinant…
We extend the work of Dyda and Kijaczko by establishing the corresponding weighted fractional Hardy inequalities with singularities on any flat submanifolds. While they derived weighted fractional Hardy inequalities with singularities at a…
We investigate the fractional Orlicz boundary Hardy-type inequality for bounded Lipschitz domains. Further, we establish fractional Orlicz boundary Hardy-type inequalities with logarithmic corrections for specific critical cases across…
We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectures posed by Frantzikinakis in [Fra10; Fra16] and obtain…
A class is studied of complex valued functions defined on the unit disk (with a possible exception of a discrete set) with the property that all their Pick matrices have not more than a prescribed number of negative eigenvalues. Functions…
Let $\Omega$ be a bounded domain of $\mathbb{R}^N$ whose boundary is a $\mathbb{C}^2$ compact manifolds. In the present paper we shall study a variational problem relating the weighted Hardy inequalities with sharp missing terms. As weights…
Multilinear trace restriction inequalities are obtained for Hardy's inequality. More generally, detailed development is given for new multilinear forms for Young's convolution inequality, and a new proof for the multilinear…
We prove a variant of the multidimensional polynomial Szemer\'edi theorem of Bergelson and Leibman where one replaces polynomial sequences with other sparse sequences defined by functions that belong to some Hardy field and satisfy certain…
In this paper we study an extension problem for the Laplace-Beltrami operator on Riemannian symmetric spaces of noncompact type and use the solution to prove Hardy-type inequalities for fractional powers of the Laplace-Beltrami operator.…
We establish endpoint bounds on a Hardy space $H^1$ for a natural class of multiparameter singular integral operators which do not decay away from the support of rectangular atoms. Hence the usual argument via a Journ\'e-type covering lemma…
In this paper, Hardy's uncertainty principle and unique continuation properties of Schrodinger equations with operator potentials in Hilbert space-valued classes are obtained. Since the Hilbert space H and linear operators are arbitrary, by…
In this note we give several characterisations of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the…
New Hardy type inequalities in sectorial area and as a limit in an exterior of a ball are proved. Sharpness of the inequalities is shown as well.
In this paper, the concept of grand variable Herz-Morrey-Hardy spaces are introduced. We also establish the atomic characterization of these spaces. As an application the authors investigate the continuity of a few singular integral…
In a very general quasilinear setting, we show that the regularizing effect of a first order term causes the existence of energy solutions for problems involving the Hardy potential and $L^1$ data. In the same setting we study sharp (local…
Motivated by previous work leveraging factorizations of second- and fourth-order differential operators, a general integral inequality involving higher order derivatives is proven by elementary means. It is then shown how this framework…
We exhibit existence of non-trivial solutions of some fractional linear Schr\"odinger equations which are radial and vanish at the origin. This is in stark contrast to what happens in the local case. We also prove analogous results in the…
We use the H\"{o}lder inequality for mixed exponents to prove some optimal variants of the generalized Hardy--Littlewood inequality for $m$-linear forms on $\ell _{p}$ spaces with mixed exponents. Our results extend recent results of Araujo…
We provide a general framework for fractional Hardy inequalities. Our framework covers, for instance, fractional inequalities related to the Dirichlet forms of some L\'evy processes, and weighted fractional inequalities on irregular open…
This note points out some bounds for the number of negative eigenvalues of Schroedinger operators with Hardy-type potentials, which follow from a simple coordinate transformation, and could prove useful in a spectral analysis of certain…