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Weighted norm inequalities for the Hardy-Littlewood maximal function

Author: Wo Sang Young
Journal: Proc. Amer. Math. Soc. 85 (1982), 24-26
MSC: Primary 42B25; Secondary 46E30
MathSciNet review: 647890
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Abstract: A characterization is obtained for weight functions $ \upsilon $ for which the Hardy-Littlewood maximal operator is bounded from $ {L^p}({{\mathbf{R}}^n},wdx)$ to $ {L^p}({{\mathbf{R}}^n},\upsilon dx)$ for some nontrivial $ w$.

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

  • [1] L. Carleson and P. W. Jones, Weighted norm inequalities and a theorem of Koosis, Mittag-Leffler Rep. No. 2, 1981.
  • [2] C. Fefferman and E. M. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107-115. MR 0284802 (44:2026)
  • [3] B. Muckenhoupt, Weighted norm inequalities for classical operators, Proc. Sympos. Pure Math., vol. 35, part 1, Amer. Math. Soc., Providence, R. I., 1979, pp. 69-83. MR 545240 (80i:42015)
  • [4] J. L. Rubio de Francia, Boundedness of maximal functions and singular integrals in weighted $ {L^p}$ spaces, Proc. Amer. Math. Soc. 83 (1981), 673-679. MR 630035 (83a:42018)

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