Download PDF - Weighted norm inequalities on spaces of homogeneous typeAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Weighted norm inequalities on spaces of homogeneous type

Authors 1

Affiliations

  1. Department of Mathematics, Hangzhou University, Hangzhou, Zhejiang 310028, People's Republic of China

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).

Bibliography

  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.
Studia Mathematica
1991-1992/101/3
Export to PBN, Opens in new tab
Pages:
241-251
Main language of publication
English
Accepted
1991-01-08
Published
1992
Exact and natural sciences