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

A maximal function characterization of the class $ H\sp{p}$


Authors: D. L. Burkholder, R. F. Gundy and M. L. Silverstein
Journal: Trans. Amer. Math. Soc. 157 (1971), 137-153
MSC: Primary 30.67
MathSciNet review: 0274767
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Abstract: Let $ u$ be harmonic in the upper half-plane and $ 0 < p < \infty $. Then $ u =$   Re$ F$ for some analytic function $ F$ of the Hardy class $ {H^p}$ if and only if the nontangential maximal function of $ u$ is in $ {L^p}$. A general integral inequality between the nontangential maximal function of $ u$ and that of its conjugate function is established.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0274767-6
PII: S 0002-9947(1971)0274767-6
Keywords: Hardy class, harmonic function, conjugate harmonic function, nontangential maximal function, Brownian motion, martingale
Article copyright: © Copyright 1971 American Mathematical Society