Results 151 to 160 of about 6,369 (172)

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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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 type inequalities associated with the Weinstein operator

Integral Transforms and Special Functions, 2019
We introduce the Riesz potential Isα associated with the Weinstein operator of order s, as Isαf(x)=1Γ(s/2)∫0∞ts/2−1Ttαf(x)dt,x∈R+d, where Ttα is its heat semigroup.
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The Hardy-Littlewood-Sobolev inequality for (\(\beta\),\(\gamma\))-distance Riesz potentials

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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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  

Reverse Stein–Weiss, Hardy–Littlewood–Sobolev, Hardy, Sobolev and Caffarelli–Kohn–Nirenberg inequalities on homogeneous groups

Forum Mathematicum, 2022
Michael Ruzhansky, Durvudkhan Suragan
exaly  

Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth

Advances in Nonlinear Analysis, 2019
Daniele Cassani, Jianjun Zhang
exaly  

Existence of the maximizing pair for the discrete Hardy-Littlewood-Sobolev inequality

Discrete and Continuous Dynamical Systems, 2015
Genggeng Huang
exaly  

On nonlocal Choquard equations with Hardy–Littlewood–Sobolev critical exponents

Journal of Mathematical Analysis and Applications, 2017
Minbo Yang
exaly