A description of weights satisfying the $A_{\infty }$ condition of Muckenhoupt
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- by Sergei V. Hruščev PDF
- Proc. Amer. Math. Soc. 90 (1984), 253-257 Request permission
Abstract:
A nonnegative weight $w$ on ${R^n}$ satisfies the ${A_\infty }$ condition iff \[ \sup \limits _{Q \in \mathcal {A}} \left ( {{{\left | Q \right |}^{ - 1}} \cdot \int _Q {wdx} } \right ) \cdot \exp \left \{ {\frac {1}{{\left | Q \right |}}\int _Q {\log \frac {1}{w}dx} } \right \} < \infty .\] Here $\mathcal {A}$ stands for a family of all cubes in ${R^n}$. Applications to BMO are considered.References
- Benjamin Muckenhoupt, The equivalence of two conditions for weight functions, Studia Math. 49 (1973/74), 101–106. MR 350297, DOI 10.4064/sm-49-2-101-106
- R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241–250. MR 358205, DOI 10.4064/sm-51-3-241-250 N. Bourbaki, Eléments de mathématique, Livre VI. Intégration, Hermann, Paris, 1952.
- R. R. Coifman and R. Rochberg, Another characterization of BMO, Proc. Amer. Math. Soc. 79 (1980), no. 2, 249–254. MR 565349, DOI 10.1090/S0002-9939-1980-0565349-8
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 90 (1984), 253-257
- MSC: Primary 42B30
- DOI: https://doi.org/10.1090/S0002-9939-1984-0727244-4
- MathSciNet review: 727244