Horizontal weighted Hardy-Rellich type inequalities on stratified Lie groups

DOI10.1007/S11785-017-0650-ZzbMath1430.22012OpenAlexW2589760020WikidataQ115377757 ScholiaQ115377757MaRDI QIDQ1656707

Bolys Sabitbek, Durvudkhan Suragan

Publication date: 10 August 2018

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-017-0650-z

zbMATH Keywords

embedding theoremSobolev type spacesCaffarelli-Kohn-Nirenberg inequalityHardy-Rellich inequalitystratified grouphorizontal estimate

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Analysis on other specific Lie groups (43A80) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (3)

Caccioppoli-type inequalities for Dirac operators ⋮ Rellich inequalities for sub-Laplacians with drift ⋮ Factorizations and Hardy-Rellich inequalities on stratified groups

Cites Work

• Quantization on nilpotent Lie groups
• Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups
• A Sobolev-Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics
• On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and \(p\)-sub-Laplacian inequalities on stratified groups
• Isoperimetric inequalities for the logarithmic potential operator
• On Hardy-Rellich type inequalities in \(\mathbb R^N\)
• Local Hardy and Rellich inequalities for sums of squares of vector fields
• Some new and short proofs for a class of Caffarelli-Kohn-Nirenberg type inequalities
• Some Hardy inequalities on the Heisenberg group
• A note on a class of Hardy-Rellich type inequalities
• Anisotropic L2-weighted Hardy and L2-Caffarelli–Kohn–Nirenberg inequalities

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