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We investigate a generalized spherical means operator, viz. generalizedspherical mean Radon transform, acting on radial functions. We establish anintegral representation of this operator and find precise estimates of thecorresponding kernel. As the main result, we prove two-weight mixed normestimates for the integral operator, with general power weights involved. Thisleads to weighted Strichartz type estimates for solutions to certain Cauchyproblems for classical Euler-Poisson-Darboux and wave equations with radialinitial data.

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