Abstract
This chapter shows how a certain square function may be used to obtain “general” multiplier and maximal multiplier theorems for radial Fourier multipliers. The multiplier theorem extends to redial multipliers of R2 that are not smooth away from a one dimensional “singularity” and the maximal theorem generalizes the results of concerning almost everywhere convergence of Bochner–Riesz means on R2 to a wider class of functions, as well as providing a unified approach to certain other operators associated to maximal and pointed convergence problem including Stein's spherical maximal function, and the solution operator to the linearized Schrodinger equation.
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