Applications of the Funk-Hecke theorem to smoothing and trace estimates

DOI10.1016/j.aim.2015.08.025zbMath1347.42017OpenAlexW1705773320MaRDI QIDQ887348

Hiroki Saito, Neal Bez, Mitsuru Sugimoto

Publication date: 28 October 2015

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

Full work available at URL: https://doi.org/10.1016/j.aim.2015.08.025

zbMATH Keywords

Fourier transformsmoothing estimatesdispersive equationstrace estimatesFunk-Hecke theorem

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) A priori estimates in context of PDEs (35B45) Harmonic analysis and PDEs (42B37)

Related Items (6)

Intermittent symmetry breaking and stability of the sharp Agmon–Hörmander estimate on the sphere ⋮ Optimal constants of smoothing estimates for the 2D Dirac equation ⋮ Stability of trace theorems on the sphere ⋮ Hardy type inequalities with spherical derivatives ⋮ Explicit uniform bounds on integrals of Bessel functions and trace theorems for Fourier transforms ⋮ Spectral identities and smoothing estimates for evolution operators

Cites Work

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• On Hartree equations with derivatives
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• Pointwise Fourier inversion and localisation in \(\mathbb{R}^n\)
• A sharp weighted \(L^2\)-estimate for the solution to the time-dependent Schrödinger equation
• Regularity, decay, and best constants for dispersive equations
• Optimal forward and reverse estimates of Morawetz and Kato-Yajima type with angular smoothing index
• Optimal constants and extremisers for some smoothing estimates
• Smoothing properties of evolution equations via canonical transforms and comparison principle
• Some Recent Progress on Sharp Kato-type Smoothing Estimates
• Local regularity of solutions to time-dependent Schrödinger equations with smooth potentials
• On the Weighted Estimate of the Solution Associated with the Schrodinger Equation
• On Turán type inequalities for modified Bessel functions
• Optimal Constant for a Smoothing Estimate of Critical Index
• Trace theorems: critical cases and best constants
• Banach spaces of solutions of the Helmholtz equation in the plane
• Regularity of solutions to the free Schrödinger equation with radial initial data
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