The structure of the reverse Hölder classes

Cruz-Uribe, David; Neugebauer, C. J.

doi:10.1090/S0002-9947-1995-1308005-6

The structure of the reverse Hölder classes
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by David Cruz-Uribe and C. J. Neugebauer

Trans. Amer. Math. Soc. 347 (1995), 2941-2960

DOI: https://doi.org/10.1090/S0002-9947-1995-1308005-6

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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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