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

 

On the Littlewood-Paley theory for mixed norm spaces


Author: John A. Gosselin
Journal: Trans. Amer. Math. Soc. 256 (1979), 113-124
MSC: Primary 42C10
MathSciNet review: 546910
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Abstract: An inequality of Littlewood-Paley type is proved for the mixed norm spaces $ {L_P}({l_r})$, $ 1 < p$, $ r < \infty $, on the interval $ [0,1]$. This result makes use of recent work by C. Fefferman and A. Cordoba on the boundedness of singular integrals on these spaces. As an application of this inequality, boundedness of the lacunary maximal partial sum operator for Walsh-Fourier series on $ {L_p}({l_r})$ is established. This result can be viewed as an extension of a similar result for the Hardy-Littlewood maximal function due to C. Fefferman and E. M. Stein.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0546910-X
PII: S 0002-9947(1979)0546910-X
Keywords: Mixed norm spaces, Littlewood-Paley function, Khinchine's inequality, Rademacher functions, Walsh-Fourier series, Hardy-Littlewood maximal function, lacunary maximal partial sum operator
Article copyright: © Copyright 1979 American Mathematical Society