Geodesic
Weighted Lorentz Norm Inequalities for the One-Sided Hardy-Littlewood Maximal Functions and for the Maximal Ergodic Operator
Canadian journal of mathematics, Tome 46 (1994) no. 5, pp. 1057-1072

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1994-060-9
Mots-clés : 42B25, 28D05, one-sided maximal functions, weighted inequalities, Lorentz spaces, ergodic averages, ergodic maximal operator, measure preserving transformations, null-preserving transformations, weights 
Salvador, P. Ortega. Weighted Lorentz Norm Inequalities for the One-Sided Hardy-Littlewood Maximal Functions and for the Maximal Ergodic Operator. Canadian journal of mathematics, Tome 46 (1994) no. 5, pp. 1057-1072. doi: 10.4153/CJM-1994-060-9
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[1] 1. Andersen, K. F., Weighted inequalities for maximal functions associated with general measures, Trans. Amer. Math. Soc. 326(1991), 907–920. Google Scholar

[2] 2. Chung, H., Hunt, R. and Kurtz, D., The Hardy-Littlewood maximal functions on L spaces with weights, Indiana Univ. Math. J. (1)31(1982), 109–120. Google Scholar

[3] 3. Hunt, R. A., On L spaces, Engseign. Math. 12(1966). Google Scholar

[4] 4. Martín-Reyes, F. J., Inequalities for the ergodic maximal function and convergence of the averages in weighted L-spaces, Trans. Amer. Math. Soc. (1) 296(1986), 61–82. Google Scholar

[5] 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] 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] 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] 8. Ortega Salvador, P., Weighted inequalities for one-sided maximal functions in Orlicz spaces, Studia Math., to appear. Google Scholar

[9] 9. Sawyer, E. T., Weighted inequalities for the one-sided Hardy-Littlewood maximal functions, Trans. Amer. Math. Soc. 297(1986), 53–61. Google Scholar

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