Results 11 to 20 of about 648,405 (147)
Affine Hardy–Littlewood–Sobolev inequalities
Journal of the European Mathematical SocietySharp affine Hardy–Littlewood–Sobolev inequalities for functions on \mathbb{R}^{n} are established, which are significantly stronger than (and directly imply) the sharp Hardy–Littlewood–Sobolev inequalities by Lieb and by Beckner, Dou, and Zhu.
Julián Eduardo Haddad, Monika Ludwig
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Sobolev and Hardy–Littlewood–Sobolev inequalities
Journal of Differential Equations, 2014 This paper is devoted to improvements of Sobolev and Onofri inequalities. The additional terms involve the dual counterparts, i.e. Hardy-Littlewood-Sobolev type inequalities. The Onofri inequality is achieved as a limit case of Sobolev type inequalities.
Jankowiak, Gaspard, Dolbeault, Jean
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Hardy-Littlewood-Sobolev inequalities via fast diffusion flows [PDF]
Proceedings of the National Academy of Sciences, 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
Carlen, EA, Carrillo, JA, Loss, M
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Sobolev and Hardy-Littlewood-Sobolev inequalities: duality and fast diffusion [PDF]
Mathematical Research Letters, 2011 In the euclidean space of dimension d ≥ 3, Sobolev and Hardy-Littlewood-Sobolev inequalities can be related by duality. We investigate how to relate these inequalities using the flow of a fast diffusion equation. Up to a term which is needed for homogeneity reasons, the difference of the two terms in Sobolev's inequality can be seen as the derivative ...
Dolbeault, Jean
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Fractional Sobolev and Hardy-Littlewood-Sobolev inequalities
, 2014 This work focuses on an improved fractional Sobolev inequality with a remainder term involving the Hardy-Littlewood-Sobolev inequality which has been proved recently. By extending a recent result on the standard Laplacian to the fractional case, we offer a new, simpler proof and provide new estimates on the best constant involved.
Jankowiak, Gaspard, Nguyen, Van Hoang
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A New, Rearrangement-free Proof of the Sharp Hardy–Littlewood–Sobolev Inequality [PDF]
, 2011 We show that the sharp constant in the Hardy-Littlewood-Sobolev inequality can be derived using the method that we employed earlier for a similar inequality on the Heisenberg group. The merit of this proof is that it does not rely on rearrangement inequalities; it is the first one to do so for the whole parameter range.
Frank, Rupert L., Lieb, Elliott H.
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The HELP inequality on trees [PDF]
, 2008 We establish analogues of Hardy and Littlewood's integro-differential equation for Schrödinger-type operators on metric and discrete trees, based on a generalised strong limit-point property of the graph ...
Brown, B. Malcolm +2 more
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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 +3 more
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Inversion positivity and the sharp Hardy–Littlewood–Sobolev inequality [PDF]
Calculus of Variations and Partial Differential Equations, 2009 We give a new proof of certain cases of the sharp HLS inequality. Instead of symmetric decreasing rearrangement it uses the reflection positivity of inversions in spheres. In doing this we extend a characterization of the minimizing functions due to Li and Zhu.
Frank, Rupert L., Lieb, Elliott H.
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Hardy-Littlewood-Sobolev inequality for $p=1$
Sbornik: Mathematics, 2022 Let $\mathcal{W}$ be a closed dilation and translation invariant subspace of the space of $\mathbb{R}^\ell$-valued Schwartz distributions in $d$ variables. We show that if the space $\mathcal{W}$ does not contain distributions of the type $a\otimes \delta_0$, $\delta_0$ being the Dirac delta, then the inequality $\|\operatorname{I}_\alpha [f]\|_{L_{d ...
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