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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Ze Lin He and David Mustard
Journal: Proc. Amer. Math. Soc. 116 (1992), 711-719
MSC: Primary 42C10; Secondary 47B35
MathSciNet review: 1099342
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1099342-4
PII: S 0002-9939(1992)1099342-4
Article copyright: © Copyright 1992 American Mathematical Society