Transference of Maximal Multipliers on Hardy Spaces

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 Rnand on Tn. More significantly, our proof shows that condition (1) in Liu and Lu's Theorem...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1995-10, Vol.123 (10), p.3169-3174
Main Authors: Fan, Dashan, Wu, Zhijian
Format: Article
Language:English
Subjects:
Continuous functions
Fourier coefficients
Integers
Mathematical theorems
Mathematics
Transference
Urelements
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Summary: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 Rnand on Tn. More significantly, our proof shows that condition (1) in Liu and Lu's Theorem 1 is superfluous.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-1995-1273491-2