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one-sided local maximal operator

Proceedings of the Edinburgh Mathematical Society (1)

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The one-sided Ap conditions and local maximal operator
Part of
- Harmonic analysis in several variables
Ana L. Bernardis, Amiran Gogatishvili, Francisco Javier Martín-Reyes, Pedro Ortega Salvador, Luboš Pick
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 55 / Issue 1 / February 2012

Published online by Cambridge University Press:

07 November 2011, pp. 79-104
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We introduce the one-sided local maximal operator and study its connection to the one-sided Ap conditions. We get a new characterization of the boundedness of the one-sided maximal operator on a quasi-Banach function space. We obtain applications to weighted Lebesgue spaces and variable-exponent Lebesgue spaces.