Related papers: Weighted anisotropic Hardy and Rellich type inequa…
The aim of this work is to study the rigidity problem for Steiner's inequality for the anisotropic perimeter, that is, the situation in which the only extremals of the inequality are vertical translations of the Steiner symmetral that we…
A new weighted Hardy-type inequality for functions from the Sobolev space $W_{p}^{1}$ is proved. It is assumed that functions vanish on small alternating pieces of the boundary. The proved inequality generalizes the classical known weighted…
The main aim of this paper is to obtain Bochkarev-type inequalities for the anisotropic grand Lorentz spaces. In the classical setting, Bochkarev obtained inequalities of the Hardy--Littlewood type, which reveal the connection between the…
We obtain several versions of the Hausdorff-Young and Hardy-Littlewood inequalities for the $(k,a)$-generalized Fourier transform recently investigated at length by Ben Sa\"i d, Kobayashi, and {\O} rsted. We also obtain a number of weighted…
In the present paper we shall improve one dimensional weighted Hardy inequalities with one-sided boundary condition by adding sharp remainders. As an application, we shall establish n dimensional weighted Hardy inequalities in a bounded…
We give necessary and sufficient conditions on a pair of positive radial functions V and W on a ball B of radius R in R^n,$n \geq 1$, so that the following inequalities hold for all $u \in C_{0}^{\infty}(B)$: $\int_{B}V(x)|\nabla u |^{2}dx…
We obtain inequalities of H\"{o}lder and Minkowski type with weights generalizing both the case of weights with alternating signs and the classical case of non-negative weights.
By employing harmonic analysis techniques, we derive weak-type Caffarelli-Kohn-Nirenberg inequalities under natural parameter conditions. A key feature of these weak-type versions is that they remain valid even at critical parameter values…
In this short article we introduce so-called anisotropic (weight) Grand Lebesgue Spaces (more exactly, Grand Lebesgue-Riesz Spaces), which are generalization of the classical Lebesgue-Riesz Spaces and ordinary Grand Lebesgue Spaces, and…
In this paper, we discuss the Hardy inequality with bilinear operators on general metric measure spaces. We give the characterization of weights for the bilinear Hardy inequality to hold on general metric measure spaces having polar…
In this paper, we study several definitions of generalized rank weights for arbitrary finite extensions of fields. We prove that all these definitions coincide, generalizing known results for extensions of finite fields.
In this paper, we derive new sharp weighted Alexandrov-Fenchel and Minkowski inequalities for smooth, closed hypersurfaces under various convexity assumptions in Euclidean, spherical, and hyperbolic spaces. These inequalities extend…
In this paper, we present a sufficient condition on a pair of nonnegative weights $v$ and $w$ such that we have a general weighted $L^{p}$-Hardy type identity. The result, for a certain choice of weights, gives weighted $L^{p}$-Hardy type…
In this paper, we establish a broad class of new sharp Alexandrov-Fenchel inequalities involving general convex weight functions for static convex hypersurfaces in hyperbolic space. Additionally, we derive new weighted Minkowski-type…
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…
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 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…
\begin{abstract} In the paper we state conditions on potentials $V$ to get the improved Hardy inequality with weight \begin{equation*} \begin{split} c_{N,\mu}\int_{\R^N}\frac{\varphi^2}{|x|^2}\mu(x)dx&+ \int_{\R^N}V\,\varphi^2\mu(x)dx…
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…
In this paper, we will prove several new inequalities of Hardy's types with explicit constants. The main results will be proved by making use of some generalizations of Opial's type inequalities and H\"older's inequality. To the best of the…