The Structure of the Reverse Hölder Classes

In this paper we study the structure of the class of functions (RHs) which satisfy the reverse Holder 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, (RH∞), whic...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 1995-08, Vol.347 (8), p.2941-2960
Main Authors: Cruz-Uribe, David, Neugebauer, Sfo, Neugebauer, C. J.
Format: Article
Language:English
Subjects:
Cubes
Factorization
Logarithms
Mathematical constants
Mathematical functions
Mathematical inequalities
Mathematical integrals
Mathematical theorems
Mathematics
Sufficient conditions
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Summary:In this paper we study the structure of the class of functions (RHs) which satisfy the reverse Holder 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, (RH∞), which plays the same role for (RHs) that the class (A1) does for the (Ap) classes.
ISSN:0002-9947
1088-6850
DOI:10.1090/s0002-9947-1995-1308005-6