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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A description of weights satisfying the $ A\sb{\infty }$ condition of Muckenhoupt


Author: Sergei V. Hruščev
Journal: Proc. Amer. Math. Soc. 90 (1984), 253-257
MSC: Primary 42B30
MathSciNet review: 727244
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Abstract: A nonnegative weight $ w$ on $ {R^n}$ satisfies the $ {A_\infty }$ condition iff

$\displaystyle \mathop {\sup }\limits_{Q \in \mathcal{A}} \left( {{{\left\vert Q... ...1}{{\left\vert Q \right\vert}}\int_Q {\log \frac{1}{w}dx} } \right\} < \infty .$

Here $ \mathcal{A}$ stands for a family of all cubes in $ {R^n}$. Applications to BMO are considered.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0727244-4
PII: S 0002-9939(1984)0727244-4
Keywords: BMO, Muckenhoupt condition
Article copyright: © Copyright 1984 American Mathematical Society