Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Transference of maximal multipliers on Hardy spaces

Authors: Da Shan Fan and Zhi Jian Wu
Journal: Proc. Amer. Math. Soc. 123 (1995), 3169-3174
MSC: Primary 42B30; Secondary 46E10
MathSciNet review: 1273491
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Abstract: Based on the atomic decomposition of the Hardy space, we give a simple proof for a theorem of Liu and Lu (Studia Math. 105 (1993), 121-134), which discusses the relation between the maximal operators on $ {\mathbb{R}^n}$ and on $ {\mathbb{T}^n}$. More significantly, our proof shows that condition (1) in Liu and Lu's Theorem 1 is superfluous.

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Keywords: Maximal operator, Hardy spaces, atomic decomposition
Article copyright: © Copyright 1995 American Mathematical Society