Two-Weight Mixed Norm Estimates for a Generalized Spherical Mean Radon Transform Acting on Radial Functions

DOI10.1137/17M1117756zbMath1377.44002arXiv1702.00760OpenAlexW2586408735MaRDI QIDQ4591199

Luz Roncal, Óscar Ciaurri, Adam Nowak

Publication date: 13 November 2017

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.00760

zbMATH Keywords

wave equationCauchy problemHankel transformStrichartz estimateradial functionEuler-Poisson-Darboux equationkernel estimateLegendre functionspherical Radon transformtwo-weight estimateaxially symmetric solutionspherical meanmixed norm estimate

Mathematics Subject Classification ID

Wave equation (35L05) Radon transform (44A12) Euler-Poisson-Darboux equations (35Q05) Harmonic analysis and PDEs (42B37)

Related Items (5)

Extension of multilinear fractional integral operators to linear operators on mixed-norm Lebesgue spaces ⋮ \(L^p -L^q\) estimates for generalized spherical averages ⋮ Endpoint estimates and optimality for the generalized spherical maximal operator on radial functions ⋮ Hardy-Littlewood-Sobolev inequality on mixed-norm Lebesgue spaces ⋮ Maximal estimates for a generalized spherical mean Radon transform acting on radial functions

Uses Software

• DLMF

Cites Work

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• Averages in the plane over convex curves and maximal operators
• The spherical maximal operator on radial functions
• Inequalities for spherically symmetric solutions of the wave equation
• Potential operators associated with Hankel and Hankel-Dunkl transforms
• Radial solutions to the wave equation
• Estimates for radial solutions to the wave equation
• A Note on the Spherical Maximal Operator for Radial Functions
• Maximal functions: Spherical means
• Hardy Inequalities with Mixed Norms
• Spherical Means and Weighted Inequalities
• The Weighted Hardy Inequality: New Proofs and the Case p = 1
• Inversion formulae for the spherical mean in odd dimensions and the Euler–Poisson–Darboux equation
• On the Equation of Euler–Poisson–Darboux

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