On first and second eigenvalues of Riesz transforms in spherical and hyperbolic geometries

DOI10.1007/s13373-016-0082-5zbMath1343.35181arXiv1603.07781OpenAlexW2964075477WikidataQ59474910 ScholiaQ59474910MaRDI QIDQ300790

Michael Ruzhansky, Durvudkhan Suragan

Publication date: 29 June 2016

Published in: Bulletin of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.07781

zbMATH Keywords

convolution operatorsRayleigh-Faber-Krahn inequality\(n\)-sphereHong-Krahn-Szegő inequalityreal hyperbolic space

Mathematics Subject Classification ID

Spectral theory and eigenvalue problems for partial differential equations (35P99) Boundary value problems for PDEs with pseudodifferential operators (35S15) Potential operators (47G40)

Related Items (12)

Isoperimetric inequalities for Schatten norms of Riesz potentials ⋮ Geometric maximizers of Schatten norms of some convolution type integral operators ⋮ Some spectral geometry inequalities for generalized heat potential operators ⋮ Remarks on the spectrum of a non‐local Dirichlet problem ⋮ On Isoperimetric Inequalities for the Cauchy-Robin Heat Operator ⋮ SOME WEAK GEOMETRIC INEQUALITIES FOR THE RIESZ POTENTIAL ⋮ Unnamed Item ⋮ Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds with negative curvature ⋮ On spectral and boundary properties of the volume potential for the Helmholtz equation ⋮ A Faber-Krahn inequality for the Riesz potential operator for triangles and quadrilaterals ⋮ Isoperimetric inequalities for the Cauchy-Dirichlet heat operator ⋮ Isoperimetric inequalities for the heat potential operator

Cites Work

• Unnamed Item
• Isoperimetric inequalities for Schatten norms of Riesz potentials
• Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
• Isoperimetric inequalities for the logarithmic potential operator
• Spherical rearrangements, subharmonic functions, and \(\ast\)-functions in \(n\)-space
• Schatten classes on compact manifolds: kernel conditions
• On the Hong-Krahn-Szego inequality for the \(p\)-Laplace operator
• Geometric maximizers of Schatten norms of some convolution type integral operators
• Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrödinger operator
• Sobolev inequalities, the Poisson semigroup, and analysis on the sphere Sn.

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