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1991-1992 | 101 | 3 | 241-251
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Weighted norm inequalities on spaces of homogeneous type

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EN
We give a characterization of the weights (u,w) for which the Hardy-Littlewood maximal operator is bounded from the Orlicz space L_Φ(u) to L_Φ(w). We give a characterization of the weight functions w (respectively u) for which there exists a nontrivial u (respectively w > 0 almost everywhere) such that the Hardy-Littlewood maximal operator is bounded from the Orlicz space L_Φ(u) to L_Φ(w).
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  • Department of Mathematics, Hangzhou University, Hangzhou, Zhejiang 310028, People's Republic of China
Bibliografia
  • [1] H. Aimar, Singular integrals and approximate identities on spaces of homogeneous type, Trans. Amer. Math. Soc. 292 (1985), 135-153.
  • [2] R. J. Bagby, Weak bounds for the maximal function in weighted Orlicz spaces, Studia Math. 95 (1990), 195-204.
  • [3] L. Carleson and P. Jones, Weighted norm inequalities and a theorem of Koosis, Mittag-Leffler Rep. No. 2, 1981.
  • [4] R. R. Coifman et G. Weiss, Analyse Harmonique Non-commutative sur Certains Espaces Homogènes, Lecture Notes in Math. 242, Springer, Berlin 1971.
  • [5] D. Gallardo, Weighted weak type integral inequalities for the Hardy-Littlewood maximal operator, Israel J. Math. 67 (1989), 95-108.
  • [6] J. Garcí a-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam 1985.
  • [7] A. E. Gatto and C. E. Gutiérrez, On weighted norm inequalities for the maximal function, Studia Math. 76 (1983), 59-62.
  • [8] A. E. Gatto, C. E. Gutiérrez and R. L. Wheeden, On weighted fractional integrals, in: Conference on Harmonic Analysis in Honor of Antoni Zygmund, Chicago 1981, Vol. I, Wadsworth, Belmont, Calif., 1983, 124-137.
  • [9] R. A. Kerman and A. Torchinsky, Integral inequalities with weights for the Hardy maximal function, Studia Math. 71 (1982), 277-284.
  • [10] J. Musielak, Orlicz Spaces and Modular Spaces, Springer, Berlin 1983.
  • [11] W. Pan, Weighted norm inequalities for fractional integrals and maximal functions on spaces of homogeneous type, Acta Sci. Natur. Univ. Pekinensis 26 (1990), 543-553.
  • [12] 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.
  • [13] E. T. Sawyer, A characterization of a two-weight norm inequality for maximal operators, Studia Math. 75 (1982), 1-11.
  • [14] W.-S. Young, Weighted norm inequalities for the Hardy-Littlewood maximal function, Proc. Amer. Math. Soc. 85 (1982), 24-26.
  • [15] M. Zhou, Weighted norm inequalities for the maximal functions on spaces of homogeneous type, Approx. Theory Appl. 6 (2) (1990), 38-42.
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bwmeta1.element.bwnjournal-article-smv101i3p241bwm
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