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A note on maximal operators and reversible weak type inequalities


Author: M. A. Leckband
Journal: Proc. Amer. Math. Soc. 92 (1984), 19-26
MSC: Primary 42B25
DOI: https://doi.org/10.1090/S0002-9939-1984-0749882-5
MathSciNet review: 749882
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Abstract: A class of maximal operators is shown to satisfy a weak type inequality and a corresponding converse inequality. The results are applicable to a fractionally iterated Hardy-Littlewood maximal operator.


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

  • [1] M. de Guzmán, Differentiation of integrals in $ {{\bf {R}}^n}$, Lecture Notes in Math., vol. 481, Springer-Verlag, New York, 1975.
  • [2] R. A. Hunt, On $ L(p,q)$-spaces, Enseign. Math. 12 (1966), 249-275. MR 0223874 (36:6921)
  • [3] W. B. Jurkat and J. L. Troutman, Maximal inequalities related to a.e. continuity, Trans. Amer. Math. Soc. 252 (1979), 49-64. MR 534110 (80h:46038)
  • [4] M. A. Leckband and C. J. Neugebauer, A general maximal operator and the $ {A_p}$-condition, Trans. Amer. Math. Soc. 275 (1983), 821-831. MR 682735 (84c:42029)
  • [5] -, Weighted iterates and variants of the Hardy-Littlewood maximal operator, Trans. Amer. Math. Soc. 279 (1983), 51-61. MR 704601 (85c:42021)
  • [6] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, N.J., 1970. MR 0290095 (44:7280)

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DOI: https://doi.org/10.1090/S0002-9939-1984-0749882-5
Article copyright: © Copyright 1984 American Mathematical Society

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