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

 

The structure of the reverse Hölder classes


Authors: David Cruz-Uribe and C. J. Neugebauer
Journal: Trans. Amer. Math. Soc. 347 (1995), 2941-2960
MSC: Primary 42B25; Secondary 46E15
MathSciNet review: 1308005
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Abstract: In this paper we study the structure of the class of functions $ (R{H_s})$ which satisfy the reverse Hölder inequality with exponent $ s > 1$. To do so we introduce a new operator, the minimal operator, which is analogous to the Hardy-Littlewood maximal operator, and a new class of functions, $ (R{H_\infty })$, which plays the same role for $ (R{H_s})$ that the class $ ({A_1})$ does for the $ ({A_p})$ classes.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1308005-6
PII: S 0002-9947(1995)1308005-6
Keywords: $ ({A_p})$ weights, reverse Hölder inequality, minimal function
Article copyright: © Copyright 1995 American Mathematical Society