Results 121 to 130 of about 648,405 (147)

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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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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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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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
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Lu, Lu, Guozhen, Tao, Chunxia
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The Hardy-Littlewood-Sobolev inequality for (\(\beta\),\(\gamma\))-distance Riesz potentials

Appl. Math. Comput., 2004
The generalized with respect to (β,γ)-distance Riesz potential defined on Sobolev space  is constructed and for this potential the theorem of Hardy–Littlewood–Sobolev type has been established.
Cinar, I, DURU, Hakkı
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A Note on the Extremizers for a Nonlinear Hardy-Littlewood-Sobolev Inequality

Journal of Information and Computing Science
The extremizers of a nonlinear Hardy-Littlewood-Sobolev inequality will be classified by making use of the Frank-Lieb argument, via the stereographic projection and spherical harmonic.
Xingdong Tang, Yang Zhang
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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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Hardy–Littlewood–Sobolev type inequalities associated with the Weinstein operator

Integral Transforms and Special Functions, 2020
Néjib Ben Salem
exaly