Two-weight mixed norm estimates for a generalized spherical mean radon transform acting on radial functions
- Ciaurri, O. 2
- Nowak, A. 3
- Roncal, L. 1
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1
Basque Center for Applied Mathematics
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2
Universidad de La Rioja
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- 3 Institute of Mathematics, Polish Academy of Sciences, Warszawa, Poland
ISSN: 0036-1410
Year of publication: 2017
Volume: 49
Issue: 6
Pages: 4402-4439
Type: Article
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Abstract
We investigate a generalized spherical means operator, in other words the generalized spherical mean Radon transform, acting on radial functions. We establish an integral representation of this operator and find precise estimates of the corresponding kernel. As the main result, we prove two-weight mixed norm estimates for the integral operator, with general power weights involved. This leads to weighted Strichartz-Type estimates for solutions to certain Cauchy problems for classical Euler{Poisson{Darboux and wave equations with radial initial data. © 2017 Society for Industrial and Applied Mathematics.