Remarks on the multiplier operators associated with a cylindrical distance function

Abstract

a b s t r a c tIn this note, we consider L p and maximal L p estimates for the generalized Riesz means which are associated with the cylindrical distance function ρWe prove these estimates up to the currently known range of the spherical Bochner-Riesz and its maximal operators. This is done by establishing implications between the corresponding estimates for the spherical Bochner-Riesz and the cylindrical multiplier operators.