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Boundedness of the maximal operator on weighted BMO

Author: Steven Bloom
Journal: Proc. Amer. Math. Soc. 94 (1985), 52-54
MSC: Primary 42B25; Secondary 42A50, 47G05
MathSciNet review: 781055
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Abstract: The Hardy-Littlewood maximal operator $ {M^*}$ is a bounded operator mapping $ {\text{BM}}{{\text{O}}_w}$, into $ {\text{BL}}{{\text{O}}_w}$ if and only if the weight $ w$ is a Reverse Hölder weight in weak $ {\alpha _2}$.

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

  • [1] S. Bloom, A commutator theorem and weighted BMO (to appear). MR 805955 (87g:42021)
  • [2] -, The maximal function on weighted BMO, Harmonic Analysis (Proc. Conf., Cortona, Italy, 1982), pp. 227-239. MR 729357 (85j:42017)
  • [3] R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241-250. MR 0358205 (50:10670)
  • [4] C. Fefferman and B. Muckenhoupt, Two nonequivalent conditions for weight functions, Proc. Amer. Math. Soc. 45 (1974), 99-104. MR 0360952 (50:13399)
  • [5] R. A. Kerman and A. Torchinsky, Integral inequalities with weights for the Hardy maximal function, Studia Math. 71 (1981/82), 277-284. MR 667316 (83k:42019)

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