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

DOI:
https://doi.org/10.1090/S0002-9947-1979-0546910-X

MathSciNet review:
546910

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Abstract | References | Similar Articles | Additional Information

Abstract: An inequality of Littlewood-Paley type is proved for the mixed norm spaces , , , on the interval . 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 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:
https://doi.org/10.1090/S0002-9947-1979-0546910-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