The type of the maximal operators of a class of Walsh convolution operators

Abstract

Abstract.This paper discusses the properties of a class of p-adic Walsh convolution operators. The class consists of those 1-parameter sets of operators with kernels that can be represented as the p-adic Walsh-Fourier integral of a uniformly quasi-convex function. The paper proves that the maximal operators associated with each 1-parameter set are all of strong type (00,00) and of weak type (1,1).