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The Class A+(g) and the One-Sided Reverse Hölder Inequality

Published online by Cambridge University Press:  20 November 2018

David Cruz-Uribe*
Affiliation:
Department of Mathematics Trinity College Hartford, CT USA 06106-3100, e-mail: [email protected]
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Abstract

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We give a direct proof that wis an A+(g) weight if and only if w satisfies a one-sided, weighted reverse Hölder inequality.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Bliedtner, J. and Loeb, P., A reduction technique for limit theorems in analysis and probability theory, Ark. Mat. 30 (1992), 2543.Google Scholar
2. Coifman, R. and Fefferman, C., Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241250.Google Scholar
3. Cruz-Uribe, D., SFO, Neugebauer, C. J. and V. Olesen, The one-sided minimal operator and the one-sided reverse Ḧolder inequality, Studia Math. 116 (1995), 255270.Google Scholar
4. Hardy, G. H. and Littlewood, J. E., A maximal theorem with function-theoretic applications, Acta Math. 54 (1930), 81116.Google Scholar
5. Martín-Reyes, F. J., New proofs of weighted inequalities for the one-sided Hardy-Littlewood maximal functions, Proc. Amer.Math. Soc. (3) 117 (1993), 691698.Google Scholar
6. Martín-Reyes, F. J., P. Ortega Salvador, and A. de la Torre, Weighted inequalities for one-sided maximal functions, Trans. Amer.Math. Soc. (2)319 (1990), 517534.Google Scholar
7. Martín-Reyes, F. J., L. Pick and A. de la Torre, A+ 1 condition, Can. J. Math. 45 (1993), 12311244.Google Scholar
8. Sawyer, E., Weighted inequalities for the one sided Hardy-Littlewood maximal functions, Trans. Amer. Math. Soc. 297 (1986), 5361.Google Scholar