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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Maximal singular integral transforms on local fields


Author: Jia Arng Chao
Journal: Proc. Amer. Math. Soc. 50 (1975), 297-302
MSC: Primary 43A70; Secondary 46J15
MathSciNet review: 0374827
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Abstract: We show that, on local fields, ``nice'' singular integral transforms preserve $ {H^p}$-spaces for $ 0 < p < \infty $ where $ {H^p}$ is the space of all distributions whose maximal functions are in $ {L^p}$. A version of the F. and M. Riesz theorem is also obtained.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0374827-4
PII: S 0002-9939(1975)0374827-4
Keywords: Local field, singular integral transform, maximal operator, $ {H^p}$-space
Article copyright: © Copyright 1975 American Mathematical Society