Sharp reversed Hardy-Littlewood-Sobolev inequality on \(\mathbf{R}^{n}\)

DOI10.1007/s11856-017-1515-xzbMath1379.26027arXiv1508.02041OpenAlexW3101243313MaRDI QIDQ2014284

Nguyen Van Hoang, Quoc-Anh Ngô

Publication date: 10 August 2017

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.02041

zbMATH Keywords

singular integral operatorHardy-Littlewood-Sobolev inequalityMarcinkiewicz interpolation theoremoptimal functionsreversed Hardy-Littlewood-Sobolev inequality

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Inequalities for sums, series and integrals (26D15)

Related Items

Classification and symmetry of positive solutions for weighted integral system, A necessary condition for certain integral equations with negative exponents, Wolff-type integral system including m equations, Classifications of positive solutions to an integral system involving the multilinear fractional integral inequality, Reverse Stein-Weiss, Hardy-Littlewood-Sobolev, Hardy, Sobolev and Caffarelli-Kohn-Nirenberg inequalities on homogeneous groups, Rearrangement Free Method for Hardy-Littlewood-Sobolev Inequalities on $\mathbb{S}^n$, Hardy–Littlewood–Sobolev inequality and existence of the extremal functions with extended kernel, Reversed Hardy-Littlewood-Sobolev inequalities with weights on the Heisenberg group, On the Wolff-type integral system with negative exponents, Liouville type theorems for general weighted integral system with negative exponents, Integral inequalities with an extended Poisson kernel and the existence of the extremals, Overdetermined problems for negative power integral equations on bounded domain, Classification of Solutions to Conformally Invariant Systems with Mixed Order and Exponentially Increasing or Nonlocal Nonlinearity, Sharp reversed Hardy–Littlewood–Sobolev inequality with extension kernel, Critical conditions and asymptotics for discrete systems of the Hardy-Littlewood-Sobolev type, Classification of Solutions to Mixed Order Elliptic System with General Nonlinearity, Classification of positive solutions for an integral system on the half space, Existence of solutions for a weighted integral equation with negative power, An extension operator on bounded domains and applications, On the existence for an integral system including \(m\) equations, Liouville type theorems for general integral system with negative exponents, Extremal problems of Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds, Negative power nonlinear integral equations on bounded domains, Classification of positive solutions to a Lane-Emden type integral system with negative exponents, Reverse Stein–Weiss inequalities and existence of their extremal functions, Symmetry and monotonicity of positive solutions for an integral system with negative exponents, Classification of solutions for an integral system with negative exponents on half space, Reverse conformally invariant Sobolev inequalities on the sphere, Subcritical approach to conformally invariant extension operators on the upper half space, Reverse Hardy-Littlewood-Sobolev inequalities, Liouville type theorem for weighted integral system with negative exponents

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Prescribing integral curvature equation.
• Sharp constants in several inequalities on the Heisenberg group
• On the integral systems with negative exponents
• Exact solutions of nonlinear conformally invariant integral equations in \(\mathbf R^3\)
• Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• Uniqueness theorem for integral equations and its application
• Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds and applications
• Symmetry and related properties via the maximum principle
• Classification of solutions of some nonlinear elliptic equations
• Competing symmetries, the logarithmic HLS inequality and Onofri's inequality on \(S^ n\)
• Best constants in Young's inequality, its converse, and its generalization to more than three functions
• Best constant in Sobolev inequality
• Problèmes isoperimetriques et espaces de Sobolev
• Remark on some conformally invariant integral equations: the method of moving spheres
• Uniqueness theorems through the method of moving spheres
• Necessary conditions for existence results of some integral system
• A symmetry problem in potential theory
• A New, Rearrangement-free Proof of the Sharp Hardy–Littlewood–Sobolev Inequality
• Reversed Hardy–Littewood–Sobolev Inequality
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Logarithmic Sobolev Inequalities
• Classification of Solutions for a System of Integral Equations
• Hardy-Littlewood-Sobolev inequalities via fast diffusion flows
• Sharp Hardy–Littlewood–Sobolev Inequality on the Upper Half Space
• On a theorem of functional analysis
• Classification of solutions for an integral equation
• Minimum Value for c in the Sobolev Inequality $\| {\phi ^3 } \|\leqq c\| {\nabla \phi } \|^3 $
• Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality