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Two-weight weak and extra-weak type inequalities for the one-sided maximal operator

Published online by Cambridge University Press:  14 November 2011

Pedro Ortega Salvador  and
Luboš Pick
Pedro Ortega Salvador
Affiliation:
Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, Campus de Teatinos, 29–71 Malaga, Spain
Luboš Pick
Affiliation:
School of Mathematics, University of Wales College of Cardiff, Senghennydd Road, Cardiff CF2 4AG, U.K.
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Synopsis

Let be the one-sided maximal operator and let Ф be a convex non-decreasing function on (0, ∞), Ф(0) = 0. We present necessary and sufficient conditions on a couple of weight functions (σ, ϱ) such that the integral inqualities of weak type

and of extra-weak type

hold. Our proofs do not refer to the theory of Orlicz spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 6 , 1993 , pp. 1109 - 1118
Copyright
Copyright © Royal Society of Edinburgh 1993

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References

1Bagby, R. J.. Weak bounds for the maximal function in weighted Orlicz spaces. Studia Math. 95 (1990), 195–204.CrossRefGoogle Scholar
2Bagby, R. J. and Parsons, J. D.. Orlicz spaces and rearranged maximal functions. Math. Nachr. 132 (1987), 15–27.CrossRefGoogle Scholar
3Gogatishvili, A. and Pick, L.. Weak and extra-weak type inequalities for the maximal operator and the Hilber transform. Czechoslovak Math. J. 43 (118) (1993), 547–566.CrossRefGoogle Scholar
4Martín-Reyes, F. J.. New proofs of weighted inequalities for the one-sided Hardy-Littlewood maximal functions. Proc. Amer. Math. Soc. 117 (1993), 691–698.CrossRefGoogle Scholar
5Martin-Reyes, F. J., Ortega Salvador, P. and de la Torre, A.. Weighted inequalities for the one-sided maximal functions. Trans. Amer. Math. Soc. 319 (1990), 517–534.CrossRefGoogle Scholar
6Martín-Reyes, F. J., Pick, L. and de la Torre, A.. A+∞(g) condition. Canad. J. Math, (to appear).Google Scholar
7Ortega Salvador, P.. Weighted inequalities for the one sided maximal functions in Orlicz spaces. Studia Math, (to appear)Google Scholar
8Pick, L.. Two weight weak type maximal inequalities in Orlicz classes. Studia Math. 100 (1991), 207–218.CrossRefGoogle Scholar
9Sawyer, E. T.. Weighted inequalities for the one sided Hardy-Littlewood maximal functions. Trans. Amer. Math. Soc. 297 (1986), 53–61.CrossRefGoogle Scholar