Results 1 to 10 of about 5,037 (196)
Hardy-Littlewood-Sobolev inequalities via fast diffusion flows. [PDF]
Proc Natl Acad Sci U S A, 2010 We give a simple proof of the λ = d - 2 cases of the sharp Hardy-Littlewood-Sobolev inequality for d ≥3, and the sharp Logarithmic Hardy-Littlewood-Sobolev inequality for d = 2 via a monotone flow governed by the fast diffusion equation.
Carlen EA, Carrillo JA, Loss M.
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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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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, Sun Wenchang
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Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains [PDF]
Journal of Inequalities and Applications, 2017 This paper is concerned with an explicit value of the embedding constant from W 1 , q ( Ω ) $W^{1,q}(\Omega)$ to L p ( Ω ) $L^{p}(\Omega)$ for a domain Ω ⊂ R N $\Omega\subset\mathbb{R}^{N}$ ( N ∈ N $N\in\mathbb{N}$ ), where 1 ≤ q ≤ p ≤ ∞ $1\leq q\leq p ...
Makoto Mizuguchi +3 more
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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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Reversed Hardy-Littlewood-Sobolev inequalities with weights on the Heisenberg group
Advances in Nonlinear Analysis, 2023 In this article, we establish some reverse weighted Hardy-Littlewood-Sobolev inequalities on the Heisenberg group. We then show the existence of extremal functions for the above inequalities by combining the subcritical approach and the renormalization ...
Hu Yunyun
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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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