Weighted norm inequalities on spaces of homogeneous type

Qiyu Sun

Studia Mathematica (1992)

  • Volume: 101, Issue: 3, page 241-251
  • ISSN: 0039-3223

Abstract

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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).

How to cite

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Sun, Qiyu. "Weighted norm inequalities on spaces of homogeneous type." Studia Mathematica 101.3 (1992): 241-251. <http://eudml.org/doc/215903>.

@article{Sun1992,
abstract = {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).},
author = {Sun, Qiyu},
journal = {Studia Mathematica},
keywords = {weights; Hardy-Littlewood maximal operator; Orlicz space},
language = {eng},
number = {3},
pages = {241-251},
title = {Weighted norm inequalities on spaces of homogeneous type},
url = {http://eudml.org/doc/215903},
volume = {101},
year = {1992},
}

TY - JOUR
AU - Sun, Qiyu
TI - Weighted norm inequalities on spaces of homogeneous type
JO - Studia Mathematica
PY - 1992
VL - 101
IS - 3
SP - 241
EP - 251
AB - 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).
LA - eng
KW - weights; Hardy-Littlewood maximal operator; Orlicz space
UR - http://eudml.org/doc/215903
ER -

References

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  1. [1] H. Aimar, Singular integrals and approximate identities on spaces of homogeneous type, Trans. Amer. Math. Soc. 292 (1985), 135-153. Zbl0578.42016
  2. [2] R. J. Bagby, Weak bounds for the maximal function in weighted Orlicz spaces, Studia Math. 95 (1990), 195-204. Zbl0718.42018
  3. [3] L. Carleson and P. Jones, Weighted norm inequalities and a theorem of Koosis, Mittag-Leffler Rep. No. 2, 1981. 
  4. [4] R. R. Coifman et G. Weiss, Analyse Harmonique Non-commutative sur Certains Espaces Homogènes, Lecture Notes in Math. 242, Springer, Berlin 1971. Zbl0224.43006
  5. [5] D. Gallardo, Weighted weak type integral inequalities for the Hardy-Littlewood maximal operator, Israel J. Math. 67 (1989), 95-108. Zbl0683.42021
  6. [6] J. Garcí a-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam 1985. 
  7. [7] A. E. Gatto and C. E. Gutiérrez, On weighted norm inequalities for the maximal function, Studia Math. 76 (1983), 59-62. Zbl0536.42021
  8. [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. [9] R. A. Kerman and A. Torchinsky, Integral inequalities with weights for the Hardy maximal function, Studia Math. 71 (1982), 277-284. Zbl0517.42030
  10. [10] J. Musielak, Orlicz Spaces and Modular Spaces, Springer, Berlin 1983. 
  11. [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. Zbl0729.42008
  12. [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. Zbl0477.42011
  13. [13] E. T. Sawyer, A characterization of a two-weight norm inequality for maximal operators, Studia Math. 75 (1982), 1-11. Zbl0508.42023
  14. [14] W.-S. Young, Weighted norm inequalities for the Hardy-Littlewood maximal function, Proc. Amer. Math. Soc. 85 (1982), 24-26. Zbl0489.42019
  15. [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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