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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 weighted norm inequalities for the Lusin area integral


Authors: Carlos Segovia and Richard L. Wheeden
Journal: Trans. Amer. Math. Soc. 176 (1973), 103-123
MSC: Primary 31A05; Secondary 30A78, 42A40
MathSciNet review: 0311921
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Abstract: It is shown that the Lusin area integral for the unit circle is a bounded operator on any weighted $ {L^p}$ space, $ 1 < p < \infty $, on which the conjugate function is a bounded operator. Results are also proved for the case $ 0 < p \leq 1$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0311921-0
PII: S 0002-9947(1973)0311921-0
Keywords: Lusin area integral, weighted norm inequalities, $ {H^p}$ spaces, Poisson integrals
Article copyright: © Copyright 1973 American Mathematical Society