Results 11 to 20 of about 6,369 (172)

Groundstates for Choquard type equations with weighted potentials and Hardy–Littlewood–Sobolev lower critical exponent

Advances in Nonlinear Analysis, 2021
We are concerned with a class of Choquard type equations with weighted potentials and Hardy–Littlewood–Sobolev lower critical ...
Zhou Shuai, Liu Zhisu, Zhang Jianjun
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Stability of Hardy-Littlewood-Sobolev inequalities with explicit lower bounds

Advances in Mathematics
Some revisions are made on its ...
Chen, Lu, Lu, Guozhen, Tang, Hanli
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Anisotropic Choquard problems with Stein–Weiss potential: nonlinear patterns and stationary waves

Comptes Rendus. Mathématique, 2021
Weighted inequality theory for fractional integrals is a relatively less known branch of calculus that offers remarkable opportunities to simulate interdisciplinary processes.
Zhang, Youpei, Tang, Xianhua, Rădulescu, Vicenţiu   +2 more
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Hardy–Littlewood–Sobolev Inequality for Upper Half Space

Annales mathématiques Blaise Pascal, 2022
We define an extension operator and study (L p ,L q ) boundedness of Hardy–Littlewood–Sobolev inequality and weighted Hardy–Littlewood–Sobolev inequality on upper Half space for the Dunkl transform.
Anoop, V. P., Parui, Sanjay
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Ground states of coupled critical Choquard equations with weighted potentials [PDF]

Opuscula Mathematica, 2022
In this paper, we are concerned with the following coupled Choquard type system with weighted potentials \[\begin{cases} -\Delta u+V_{1}(x)u=\mu_{1}(I_{\alpha}\!\ast\![Q(x)|u|^{\frac{N+\alpha}{N}}])Q(x)|u|^{\frac{\alpha}{N}-1}u+\beta(I_{\alpha}\!\ast\![Q(
Gaili Zhu, Chunping Duan, Jianjun Zhang, Huixing Zhang   +3 more
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Hardy–Littlewood–Sobolev and related inequalities: Stability

, 2022
The purpose of this text is twofold. We present a review of the existing stability results for Sobolev, Hardy-Littlewood-Sobolev (HLS) and related inequalities. We also contribute to the topic with some observations on constructive stability estimates for (HLS).
Dolbeault, Jean, Esteban, Maria J.
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Integral inequalities with an extended Poisson kernel and the existence of the extremals

Advanced Nonlinear Studies, 2023
In this article, we first apply the method of combining the interpolation theorem and weak-type estimate developed in Chen et al. to derive the Hardy-Littlewood-Sobolev inequality with an extended Poisson kernel.
Tao Chunxia, Wang Yike
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Sharp Hardy–Littlewood–Sobolev inequalities on quaternionic Heisenberg groups [PDF]

Nonlinear Analysis, 2016
26 ...
Christ, Michael, Liu, Heping, Zhang, An
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Sharp reversed Hardy-Littlewood-Sobolev inequality on $\mathbb R^n$ [PDF]

Israel Journal of Mathematics, 2015
This is the first in our series of papers concerning some Hardy-Littlewood-Sobolev type inequalities. In the present paper, the main objective is to establish the following sharp reversed HLS inequality in the whole space $\mathbb R^n$ \[\int_{\mathbb R^n} \int_{\mathbb R^n} f(x) |x-y|^ g(y) dx dy \geqslant \mathscr C_{n,p,r} \|f\|_{L^p (\mathbb R^n)}\
Ngô, Quoc Anh, Nguyen, Van Hoang
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Reversed Stein–Weiss Inequalities with Poisson-Type Kernel and Qualitative Analysis of Extremal Functions

Advanced Nonlinear Studies, 2021
Through conformal map, isoperimetric inequalities are equivalent to the Hardy–Littlewood–Sobolev (HLS) inequalities involved with the Poisson-type kernel on the upper half space.
Tao Chunxia
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