\(p\)-Bessel pairs, Hardy's identities and inequalities and Hardy-Sobolev inequalities with monomial weights

DOI10.1007/s12220-021-00847-2zbMath1482.42058OpenAlexW4210756227MaRDI QIDQ2075354

Guozhen Lu, Nguyen Tuan Duy, Lam Hoang Nguyen

Publication date: 14 February 2022

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-021-00847-2

zbMATH Keywords

Hardy inequalityHardy-Sobolev inequality\(p\)-Bessel pairmonomial weight

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities involving derivatives and differential and integral operators (26D10) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23) Harmonic analysis and PDEs (42B37)

Related Items

\(L^p\) Hardy's identities and inequalities for Dunkl operators ⋮ Hardy-Sobolev inequalities with Dunkl weights ⋮ Weighted Hardy-Sobolev, log-Sobolev and Moser-Onofri-Beckner inequalities with monomial weights ⋮ Improved \(L^p\)-Hardy and \(L^p\)-Rellich inequalities with magnetic fields ⋮ Caffarelli-Kohn-Nirenberg identities, inequalities and their stabilities ⋮ Sharp Hardy identities and inequalities on Carnot groups ⋮ Hardy-Poincaré-Sobolev type inequalities on hyperbolic spaces and related Riemannian manifolds ⋮ Hardy's identities and inequalities on Cartan-Hadamard manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The analysis and geometry of Hardy's inequality
• Sharp isoperimetric inequalities via the ABP method
• Best constants and existence of maximizers for weighted Trudinger-Moser inequalities
• Hardy-Sobolev-type inequalities with monomial weights
• Bessel pairs and optimal Hardy and Hardy-Rellich inequalities
• Sharp Hardy-Sobolev inequalities
• Sharp weighted isoperimetric and Caffarelli-Kohn-Nirenberg inequalities
• Critical Hardy--Sobolev inequalities
• Nonlinear ground state representations and sharp Hardy inequalities
• Estimates on Moser embedding
• The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential
• Seventy five (thousand) unsolved problems in analysis and partial differential equations
• Sharp weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg inequalities and their extremal functions
• Sharp Hardy identities and inequalities on Carnot groups
• Improved Hardy and Hardy-Rellich type inequalities with Bessel pairs via factorizations
• Green's functions of Paneitz and GJMS operators on hyperbolic spaces and sharp Hardy-Sobolev-Maz'ya inequalities on half spaces
• Hardy-Poincaré-Sobolev type inequalities on hyperbolic spaces and related Riemannian manifolds
• Geometric Hardy's inequalities with general distance functions
• On Hardy and Caffarelli-Kohn-Nirenberg inequalities
• Sharp Caffarelli-Kohn-Nirenberg-type inequalities on Carnot groups
• Factorizations and Hardy's type identities and inequalities on upper half spaces
• Sharp constants and optimizers for a class of Caffarelli-Kohn-Nirenberg inequalities
• Sharp Trudinger-Moser inequalities with monomial weights
• The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three-dimensional upper half space
• Sobolev and isoperimetric inequalities with monomial weights
• Weighted Hardy-Sobolev, log-Sobolev and Moser-Onofri-Beckner inequalities with monomial weights
• Improved Multipolar Hardy Inequalities
• Pitt's inequality and the fractional Laplacian: Sharp error estimates
• Optimal Hardy inequalities in cones
• Hardy inequalities with optimal constants and remainder terms
• A unified approach to improved $L^p$ Hardy inequalities with best constants
• Factorizations and Hardy–Rellich-type inequalities
• Functional Inequalities: New Perspectives and New Applications
• Regularity of Stable Solutions up to Dimension 7 in Domains of Double Revolution
• Analysis and Geometry of Markov Diffusion Operators
• General sharp weighted Caffarelli–Kohn–Nirenberg inequalities
• Paneitz operators on hyperbolic spaces and high order Hardy-Sobolev-Maz'ya inequalities on half spaces
• Sharp weighted Sobolev and Gagliardo–Nirenberg inequalities on half-spaces via mass transport and consequences
• Hardy's inequality with weights
• Radial and logarithmic refinements of Hardy’s inequality
• Sobolev Spaces