Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-24T05:30:49.187Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  20 November 2018

David Cruz-Uribe
David Cruz-Uribe*
Affiliation:
Department of Mathematics Trinity College Hartford, CT USA 06106-3100, e-mail: david.cruzuribe@mail.trincoll.edu
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.

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

Keywords

Primary: 42B25one-sided maximal operatorone-sided (A∞)one-sided reverse Hölder inequality
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 2 , 01 June 1997 , pp. 169 - 173
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), 25–43.Google Scholar
2. Coifman, R. and Fefferman, C., Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241–250.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), 255–270.Google Scholar
4. Hardy, G. H. and Littlewood, J. E., A maximal theorem with function-theoretic applications, Acta Math. 54 (1930), 81–116.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), 691–698.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), 517–534.Google Scholar
7. Martín-Reyes, F. J., L. Pick and A. de la Torre, A+ 1 condition, Can. J. Math. 45 (1993), 1231–1244.Google Scholar
8. Sawyer, E., Weighted inequalities for the one sided Hardy-Littlewood maximal functions, Trans. Amer. Math. Soc. 297 (1986), 53–61.Google Scholar