Maximal singular integral transforms on local fields

Chao, Jia Arng

doi:10.1090/S0002-9939-1975-0374827-4

Maximal singular integral transforms on local fields
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Proc. Amer. Math. Soc. 50 (1975), 297-302 Request permission

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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