Two-weight mixed norm estimates for a generalized spherical mean Radon transform acting on radial functions
Classical Analysis and ODEs
2018-11-06 v1
Abstract
We investigate a generalized spherical means operator, viz. 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.
Cite
@article{arxiv.1702.00760,
title = {Two-weight mixed norm estimates for a generalized spherical mean Radon transform acting on radial functions},
author = {Óscar Ciaurri and Adam Nowak and Luz Roncal},
journal= {arXiv preprint arXiv:1702.00760},
year = {2018}
}
Comments
38 pages, 5 figures