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

He, Ze Lin; Mustard, David

doi:10.1090/S0002-9939-1992-1099342-4

The type of the maximal operators of a class of Walsh convolution operators
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by Ze Lin He and David Mustard

Proc. Amer. Math. Soc. 116 (1992), 711-719

DOI: https://doi.org/10.1090/S0002-9939-1992-1099342-4

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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 $(\infty ,\infty )$ and of weak type $(1,1)$.

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