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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42B30

Retrieve articles in all journals with MSC: 42B30

Additional Information

Keywords: BMO, Muckenhoupt condition
Article copyright: © Copyright 1984 American Mathematical Society