Arkiv för Matematik

, Volume 33, Issue 2, pp 377–384 | Cite as

Weak type estimates for some maximal operators on the weighted Hardy spaces

  • Shuichi Sato


Weighted weak type estimates are proved for some maximal operators on the weighted Hardy spacesH ω p (0 <p < 1, ω ∈A 1) (0<p<1, ω∞A1); in particular, weighted weak type endpoint estimates are obtained for the maximal operators arising from the Bochner-Riesz means and the spherical means onH ω p .


Hardy Space Maximal Operator Weak Type Atomic Decomposition Weight Norm Inequality 
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  1. 1.
    Christ, M., Weak type endpoint bounds for Bochner-Riesz multipliers,Rev. Mat. Iberoamericana 3 (1987), 25–31.MathSciNetGoogle Scholar
  2. 2.
    Christ, M., Weak type (1, 1) bounds for rough operators,Ann. of Math. 128 (1988), 19–42.CrossRefMathSciNetGoogle Scholar
  3. 3.
    Christ, M. andRubio De Francia, J. L., Weak type (1, 1) bounds for rough operators, II,Invent. Math. 93 (1988), 225–237.CrossRefMathSciNetGoogle Scholar
  4. 4.
    Garcia-Cuerva, J. andRubio De Francia, J. L.,Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam-New York-Oxford, 1985.zbMATHGoogle Scholar
  5. 5.
    Sato, S., Spherical summability and a vector-valued inequality, to appear inBull. London Math. Soc. Google Scholar
  6. 6.
    Sato, S., A weighted vector-valued weak type (1, 1) inequality and spherical summation, to appear inStudia Math. Google Scholar
  7. 7.
    Seeger, A., Endpoint estimates for multiplier transformations on compact manifold,Indiana Univ. Math. J. 40 (1991), 471–533.CrossRefMathSciNetGoogle Scholar
  8. 8.
    Stein, E. M., Taibleson, M. H. andWeiss, G., Weak type estimates for maximal operators on certainH p classes,Rend. Circ. Mat. Palermo 2 (1981), suppl. 1, 81–97.MathSciNetGoogle Scholar
  9. 9.
    Strömberg, J.-O. andTorchinsky, A.,Weighted Hardy Spaces, Lecture Notes in Math.1381, Springer-Verlag, Berlin-Heidelberg, 1989.zbMATHGoogle Scholar
  10. 10.
    Taibleson, M. H. andWeiss, G., The molecular characterization of certain Hardy spaces,Astérisque 77 (1980), 67–149.MathSciNetGoogle Scholar
  11. 11.
    Vargas, A., Weighted weak type (1, 1) bounds for rough operators,Preprint.Google Scholar

Copyright information

© Institut Mittag-Leffler 1995

Authors and Affiliations

  • Shuichi Sato
    • 1
  1. 1.Department of Mathematics Faculty of EducationKanazawa UniversityKanazawaJapan

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