A note on the strong maximal function
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- by Richard J. Bagby PDF
- Proc. Amer. Math. Soc. 88 (1983), 648-650 Request permission
Abstract:
Given a nonnegative measurable function $f$ on ${R^2}$ which is integrable over sets of finite measure, we construct a new function $g$ with the same distribution function as $f$ such that the strong maximal function of $g$ has the same local integrability properties as its Hardy-Littlewood maximal function.References
- Richard J. Bagby, Maximal functions and rearrangements: some new proofs, Indiana Univ. Math. J. 32 (1983), no. 6, 879–891. MR 721570, DOI 10.1512/iumj.1983.32.32060
- N. A. Fava, E. A. Gatto, and C. Gutiérrez, On the strong maximal function and Zygmund’s class $L(\textrm {log}^{+}L)^{n}$, Studia Math. 69 (1980/81), no. 2, 155–158. MR 604348, DOI 10.4064/sm-69-2-155-158 B. Jessen, J. Marcinkiewicz and A. Zygmund, Note on the differentiability of multiple integrals, Fund. Math. 25 (1935), 217-234.
- E. M. Stein, Note on the class $L$ $\textrm {log}$ $L$, Studia Math. 32 (1969), 305–310. MR 247534, DOI 10.4064/sm-32-3-305-310
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 648-650
- MSC: Primary 42B25
- DOI: https://doi.org/10.1090/S0002-9939-1983-0702293-X
- MathSciNet review: 702293