Results 171 to 180 of about 5,037 (196)

Sharp reversed Hardy–Littlewood–Sobolev inequality with extension kernel

Studia Mathematica, 2023
Summary: In this paper, we prove the following reversed Hardy-Littlewood-Sobolev inequality with extension kernel: \[ \int_{\mathbb{R}_+^n}\int_{\partial\mathbb{R}^n_+}\frac{x_n^\beta}{|x-y|^{n-\alpha}}f(y)g(x)\,dy\,dx\geq C_{n,\alpha ,\beta ,p}\|f\|_{L^p(\partial\mathbb{R}_+^n)}\|g\|_{L^{q^\prime}(\mathbb{R}_+^n)} \] for any nonnegative functions \(f ...
Dai, Wei, Hu, Yunyun, Liu, Zhao
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On the shape of solutions to an integral system related to the weighted Hardy–Littlewood–Sobolev inequality

Journal of Mathematical Analysis and Applications, 2012
We study the Euler–Lagrange system for a variational problem associated with the weighted Hardy–Littlewood–Sobolev inequality. We show that all the nonnegative solutions to the system are radially symmetric and have particular profiles around the origin ...
Onodera, Michiaki, Michiaki Onodera
exaly   +2 more sources

Extension of Hardy–Littlewood–Sobolev Inequalities for Riesz Potentials on Hypergroups

Mediterranean Journal of Mathematics, 2020
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Idha Sihwaningrum, Sri Maryani, Hendra Gunawan   +2 more
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Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities

The Annals of Mathematics, 1983
A maximizing function, f, is shown to exist for the HLS inequality on R': 11 IXI - * fIq < Np f A , Iif IIwith Nbeing the sharp constant and i/p + X/n = 1 + 1/q, 1
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Hardy–Littlewood–Sobolev inequality and existence of the extremal functions with extended kernel

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2022
In this paper, we consider the following Hardy–Littlewood–Sobolev inequality with extended kernel(0.1)\begin{equation} \int_{\mathbb{R}_+^{n}}\int_{\partial\mathbb{R}^{n}_+} \frac{x_n^{\beta}}{|x-y|^{n-\alpha}}f(y)g(x) {\rm d}y{\rm d}x\leq C_{n,\alpha,\beta,p}\|f\|_{L^{p}(\partial\mathbb{R}_+^{n})} \|g\|_{L^{q'}(\mathbb{R}_+^{n})}, \end{equation}for ...
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On discrete reversed Hardy–Littlewood–Sobolev inequalities

Canadian Mathematical Bulletin
Abstract Recently, the discrete reversed Hardy–Littlewood–Sobolev inequality with infinite terms was proved. In this article, we study the attainability of its best constant. For this purpose, we introduce a discrete reversed Hardy–Littlewood–Sobolev inequality with finite terms. The constraint of parameters of this inequality is more
Tiantian Zhou, Yutian Lei
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Weighted Hardy–Littlewood–Sobolev inequalities on the upper half space

Communications in Contemporary Mathematics, 2016
In this paper, we establish a weighted Hardy–Littlewood–Sobolev (HLS) inequality on the upper half space using a weighted Hardy type inequality on the upper half space with boundary term, and discuss the existence of extremal functions based on symmetrization argument.
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Hardy—Littlewood—Sobolev Inequalities with the Fractional Poisson Kernel and Their Applications in PDEs

Acta Mathematica Sinica, English Series, 2019
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Chen, Lu, Lu, Guozhen, Tao, Chunxia
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Weighted Hardy-Littlewood-Sobolev Inequality on the Unit Sphere

2013
One of the main aims in this thesis is to establish analogues of the classical Hardy-Littlewood-Sobolev (HLS) inequality for weighted orthogonal polynomial expansions (WOPEs) on the unit sphere, the unit ball and the simplex. An optimal condition for which this inequality holds is obtained.
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The Hardy-Littlewood-Sobolev inequality for non-isotropic Riesz potentials

1997
Let \(\lambda_1,\lambda_2,\dots, \lambda_n\) be positive numbers with \(|\lambda|= \sum^n_{i=1} \lambda_i\) and \[ |x|_\lambda= \Biggl( \sum^n_{i=1}|x_i|^{{1\over\lambda_i}}\Biggr)^{|\lambda|/n},\quad x\in\mathbb{R}^n. \] Let us define the non-isotropic Riesz potential \[ \Lambda_\alpha f(x)= \int_{\mathbb{R}^n}|x-y|^{\alpha- n}_\lambda f(y)dy;\quad 00\
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