# Two-weight mixed norm estimates for a generalized spherical mean Radon transform acting on radial functions

## TL;DR

This paper derives two-weight mixed norm estimates for a generalized spherical mean Radon transform on radial functions, leading to weighted Strichartz estimates for related PDEs with radial initial data.

## Contribution

It provides the first precise kernel estimates and establishes new weighted norm inequalities for the generalized spherical mean Radon transform.

## Key findings

- Established integral representation of the operator
- Derived sharp kernel estimates
- Proved weighted Strichartz type estimates for PDE solutions

## 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.