Related papers: Magnetic Hardy inequalities with singular integral…
We find best constants in several dilation invariant integral inequalities involving derivatives of functions. Some of these inequalities are new and some were known without best constants. The contents: 1. Estimate for a quadratic form of…
We obtain new variants of weighted Gagliardo-Nirenberg interpolation inequalities in Orlicz spaces, as a consequence of weighted Hardy-type inequalities. The weights we consider need not be doubling.
Sharp extensions of Pitt's inequality and bounds for Stein-Weiss fractional integrals are obtained that incorporate gradient forms and vector-valued operators. Such results include Hardy-Rellich inequalities.
We consider here the magneto-hydrodynamics (MHD) equations on the whole space. For the 3D case, in the setting of the weighted $L^2$ spaces we obtain a weak-strong uniqueness criterion provided that the velocity field and the magnetic field…
In this paper, we focus on three main objectives related to Hardy-type inequalities on Cartan-Hadamard manifolds. Firstly, we explore critical Hardy-type inequalities that contain logarithmic terms, highlighting their significance.…
In this article we first establish a complete characterization of Hardy's inequalities in $\mathbb{R}^n$ involving distances to different codimension subspaces. In particular the corresponding potentials have strong interior singularities.…
Let M be an N-function satisfying the $\Delta_2$- condition, let $\omega, \vp$ be two other functions, $\omega\ge 0$. We study Hardy-type inequalities \[ \int_{\rp} M(\omega (x)|u(x)|) {\rm exp}(-\vp (x))dx \le C\int_{\rp} M(|u'(x)|) {\rm…
The main purpose of this article is to obtain (weighted) fractional Hardy inequalities with a remainder and fractional Hardy-Sobolev-Maz'ya inequalities valid for $1<p<2$.
The main results in the paper are the weighted multipolar Hardy inequalities \begin{equation*} c\int_{\R^N}\sum_{i=1}^n\frac{u^2}{|x-a_i|^2}\,d\mu \leq\int_{\R^N}|\nabla u |^2d\mu+ K\int_{\R^N} u^2d\mu, \end{equation*} in $\R^N$ for any $u$…
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 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 establish fractional Hardy inequality on bounded domains in $\mathbb{R}^{d}$ with inverse of distance function from smooth boundary of codimension $k$, where $k=2, \dots,d$, as weight function. The case $sp=k$ is the critical case, where…
We give new proofs of Hardy space estimates for fractional and singular integral operators on weighted and variable exponent Hardy spaces. Our proofs consist of several interlocking ideas: finite atomic decompositions in terms of $L^\infty$…
In this paper we state the weighted Hardy inequality \begin{equation*} c\int_{{\mathbb R}^N}\sum_{i=1}^n \frac{\varphi^2 }{|x-a_i|^2}\, \mu(x)dx\le \int_{{\mathbb R}^N} |\nabla\varphi|^2 \, \mu(x)dx +k \int_{\mathbb{R}^N}\varphi^2 \,…
We construct new optimal $L^p$ Hardy-type inequalities for elliptic Schr\"odinger-type operators
In this article we study some new pointwise inequalities between rough singular integral operators, weighted maximal functions of the gradient and weighted Morrey spaces. These pointwise estimates will naturally lead us to a new class of…
We study Hardy-type inequalities on infinite homogeneous trees. More precisely, we derive optimal Hardy weights for the combinatorial Laplacian in this setting and we obtain, as a consequence, optimal improvements for the Poincar\'e…
In this paper, we study certain inequalities and a related result for weighted Sobolev spaces on H\"older-$\alpha$ domains, where the weights are powers of the distance to the boundary. We obtain results regarding the divergence equation's…
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 analyze the dispersive properties of a Dirac system perturbed with a magnetic field. We prove a general virial identity; as applications, we obtain smoothing and endpoint Strichartz estimates which are optimal from the decay point of…