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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Norm inequalities for the Littlewood-Paley function $ g\sp{\ast} \sb{\lambda }$


Authors: Benjamin Muckenhoupt and Richard L. Wheeden
Journal: Trans. Amer. Math. Soc. 191 (1974), 95-111
MSC: Primary 44A15; Secondary 30A78, 42A92
MathSciNet review: 0387973
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Abstract: Weighted norm inequalities for $ {L^p}$ and $ {H^p}$ are derived for the Littlewood-Paley function $ g_\lambda ^ \ast $. New results concerning the boundedness of this function are obtained, by a different method of proof, even in the unweighted case. The proof exhibits a connection between $ g_\lambda ^\ast$ and a maximal function for harmonic functions which was introduced by C. Fefferman and E. M. Stein. A new and simpler way to determine the behavior of this maximal function is given.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0387973-X
PII: S 0002-9947(1974)0387973-X
Article copyright: © Copyright 1974 American Mathematical Society