Fourier analysis and optimal Hardy-Adams inequalities on hyperbolic spaces of any even dimension

DOI10.1016/j.aim.2018.05.035zbMath1402.46025OpenAlexW2807254072WikidataQ129736242 ScholiaQ129736242MaRDI QIDQ1649336

Guozhen Lu, Jun-Gang Li, Qiao-Hua Yang

Publication date: 5 July 2018

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2018.05.035

zbMATH Keywords

Hardy inequalitiesAdams' inequalitiesBessel-Green-Riesz kernelsFourier analysis on hyperbolic spacesfractional Laplacians on hyperbolic spaces

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (38)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sharp Moser-Trudinger inequalities on Riemannian manifolds with negative curvature
• Sharp Moser-Trudinger inequalities on hyperbolic spaces with exact growth condition
• Sharp singular Trudinger-Moser inequalities in Lorentz-Sobolev spaces
• An interpolation of Hardy inequality and Moser-Trudinger inequality on Riemannian manifolds with negative curvature
• Sharp higher-order Sobolev inequalities in the hyperbolic space \(\mathbb H^n\)
• Explicit formulas for GJMS-operators and \(Q\)-curvatures
• A Hardy-Moser-Trudinger inequality
• Sharp Adams type inequalities in Sobolev spaces \(W^{m,\frac{n}{m}}(\mathbb R^n)\) for arbitrary integer \(m\)
• The \(Q\)-curvature on a 4-dimensional Riemannian manifold \((M,g)\) with \(\int_M QdV_g = 8\pi^2\)
• A sharp Trudinger-Moser inequality on any bounded and convex planar domain
• Sharp affine and improved Moser-Trudinger-Adams type inequalities on unbounded domains in the spirit of Lions
• Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
• Trudinger-Moser inequalities on complete noncompact Riemannian manifolds
• Some constructions for the fractional Laplacian on noncompact manifolds
• Adams inequality on the hyperbolic space
• Adams' inequalities for bi-Laplacian and extremal functions in dimension four
• Affine Moser-Trudinger and Morrey-Sobolev inequalities
• A sharp inequality of J. Moser for higher order derivatives
• \(\mathbb{L}_ p\) Fourier multipliers on Riemannian symmetric spaces of the noncompact type
• Sharp borderline Sobolev inequalities on compact Riemannian manifolds
• Equivalence of critical and subcritical sharp Trudinger-Moser-Adams inequalities
• Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications
• Heat kernel and Green function estimates on noncompact symmetric spaces
• Sharp Hardy-Adams inequalities for bi-Laplacian on hyperbolic space of dimension four
• Extremal functions for Moser-Trudinger type inequality on compact closed 4-manifolds
• Remarks on the extremal functions for the Moser-Trudinger inequality
• Convolution operators and L(p, q) spaces
• A new approach to sharp Moser-Trudinger and Adams type inequalities: a rearrangement-free argument
• Sharp subcritical Moser-Trudinger inequalities on Heisenberg groups and subelliptic PDEs
• On the Grushin operator and hyperbolic symmetry
• Trudinger–Moser inequality in the hyperbolic space ℍN
• Best Constants for Adams’ Inequalities with the Exact Growth Condition in ℝⁿ
• A Trudinger Inequality on Surfaces with Conical Singularities
• Heat Kernel Bounds on Hyperbolic Space and Kleinian Groups
• The Heat Kernel on Hyperbolic Space
• The Hardy–Rellich inequality for polyharmonic operators
• Sharp Adams-type inequalities in ℝⁿ
• Sharp Adams and Hardy-Adams inequalities of any fractional order on hyperbolic spaces of all dimensions
• Generalized Helgason-Fourier transforms associated to variants of the Laplace-Beltrami operators on the unit ball in $\mathbb{R}^{n}$
• The Nonlinear Schrödinger Equation on Hyperbolic Space
• Adams' Inequality with the Exact Growth Condition in ℝ⁴

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