Results 1 to 10 of about 142 (136)
Hardy–Littlewood–Sobolev Inequality on Mixed-Norm Lebesgue Spaces [PDF]
Journal of Geometric Analysis, 2022 We consider the Hardy-Littlewood-Sobolev inequality on mixed-norm Lebesgue spaces. We give a complete characterization of indices $\vec p$ and $\vec q$ such that the Riesz potential is bounded from $L^{\vec p}$ to $L^{\vec q}$, including all the endpoint cases. As a result, we get the mixed-norm Hardy-Littlewood-Sobolev inequality.
Wenchang Sun
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Martingale Transforms and the Hardy-Littlewood-Sobolev Inequality for Semigroups [PDF]
Potential Analysis, 2016 We give a representation of the fractional integral for symmetric Markovian semigroups as the projection of martingale transforms and prove the Hardy-Littlewood-Sobolev(HLS) inequality based on this representation. The proof rests on a new inequality for a fractional Littlewood-Paley $g$-function.
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Hardy–Littlewood–Sobolev and Stein–Weiss inequalities on homogeneous Lie groups [PDF]
Integral Transforms and Special Functions, 2019 In this note we prove the Stein-Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogeneous norms play a key role in our proofs. Also, we give a simple proof of the Hardy-Littlewood-Sobolev inequality on general homogeneous Lie groups.
Michael Ruzhansky, Durvudkhan Suragan
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Generalized Logarithmic Hardy–Littlewood–Sobolev Inequality [PDF]
International Mathematics Research Notices, 2020 Abstract This paper is devoted to logarithmic Hardy–Littlewood–Sobolev inequalities in the 2D Euclidean space, in the presence of an external potential with logarithmic growth. The coupling with the potential introduces a new parameter, with two regimes.
Dolbeault, Jean, Li, Xingyu
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Nonlinear Choquard equations on hyperbolic space [PDF]
Opuscula Mathematica, 2022 In this paper, our purpose is to prove the existence results for the following nonlinear Choquard equation \[-\Delta_{\mathbb{B}^{N}}u=\int_{\mathbb{B}^N}\dfrac{|u(y)|^{p}}{|2\sinh\frac{\rho(T_y(x))}{2}|^\mu} dV_y \cdot |u|^{p-2}u +\lambda u\] on the ...
Haiyang He
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Solutions for nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities
Advances in Nonlinear Analysis, 2022 In this article, we aimed to study a class of nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities as well as critical Hardy nonlinearities in RN{{\mathbb{R}}}^{N}.
Tao Mengfei, Zhang Binlin
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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
Anoop, V. P., Parui, Sanjay
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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 +2 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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