Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-20T14:24:13.705Z Has data issue: false hasContentIssue false
  • English
  • Français

Weighted Lorentz Norm Inequalities for the One-Sided Hardy-Littlewood Maximal Functions and for the Maximal Ergodic Operator

Published online by Cambridge University Press:  20 November 2018

P. Ortega Salvador
P. Ortega Salvador*
Affiliation:
Análisis Matemático Facultad de Ciencias, Universidad de Málaga, 29071-Malaga, Spain
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we characterize weighted Lorentz norm inequalities for the one sided Hardy-Littlewood maximal function

Similar questions are discussed for the maximal operator associated to an invertible measure preserving transformation of a measure space.

Keywords

42B2528D05one-sided maximal functionsweighted inequalitiesLorentz spacesergodic averagesergodic maximal operatormeasure preserving transformationsnull-preserving transformationsweights
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 5 , 01 October 1994 , pp. 1057 - 1072
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Andersen, K. F., Weighted inequalities for maximal functions associated with general measures, Trans. Amer. Math. Soc. 326(1991), 907–920.Google Scholar
2. Chung, H., Hunt, R. and Kurtz, D., The Hardy-Littlewood maximal functions on Lp,q spaces with weights, Indiana Univ. Math. J. (1)31(1982), 109–120.Google Scholar
3. Hunt, R. A., On Lp,q spaces, Engseign. Math. 12(1966).Google Scholar
4. Martín-Reyes, F. J., Inequalities for the ergodic maximal function and convergence of the averages in weighted Lp-spaces, Trans. Amer. Math. Soc. (1) 296(1986), 61–82.Google Scholar
5. Martín-Reyes, F. J., New proofs of weighted inequalities for the one sided Hardy-Littlewood maximal functions, Proc. Amer. Math. Soc, to appear.Google Scholar
6. Martín-Reyes, F. J., Ortega Salvador, P. and de la Torre, A., Weighted inequalities for one-sided maximal functions, Trans. Amer. Math. Soc. (2) 319(1990), 517–534.Google Scholar
7. Ortega Salvador, P., Weights for the ergodic maximal operator and a.e. convergence of the ergodic averages for functions in Lorentz spaces, Tôhoku Math. J. 45(1993), 437–446.Google Scholar
8. Ortega Salvador, P., Weighted inequalities for one-sided maximal functions in Orlicz spaces, Studia Math., to appear.Google Scholar
9. Sawyer, E. T., Weighted inequalities for the one-sided Hardy-Littlewood maximal functions, Trans. Amer. Math. Soc. 297(1986), 53–61.Google Scholar