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The one-sided Ap conditions and local maximal operator

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  07 November 2011

Ana L. Bernardis ,
Amiran Gogatishvili ,
Francisco Javier Martín-Reyes ,
Pedro Ortega Salvador  and
Luboš Pick
Ana L. Bernardis
Affiliation:
Instituto de Matemática Aplicada del Litoral (CONICET), Facultad de Ingeniería Química (UNL), Güemes 3450, (3000) Santa Fe, Argentina (bernard@santafe-conicet.gov.ar)
Amiran Gogatishvili
Affiliation:
Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 11567 Praha 1, Czech Republic (gogatish@math.cas.cz)
Francisco Javier Martín-Reyes
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain (martin_reyes@uma.es; portega@uma.es)
Pedro Ortega Salvador
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain (martin_reyes@uma.es; portega@uma.es)
Luboš Pick
Affiliation:
Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675 Praha 8, Czech Republic (pick@karlin.mff.cuni.cz)
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Abstract

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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.

Keywords

one-sided Ap conditionsone-sided local maximal operatorquasi-Banach function spacesvariable-exponent Lebesgue spaces

MSC classification

Secondary: 42B25: Maximal functions, Littlewood-Paley theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 1 , February 2012 , pp. 79 - 104
Copyright
Copyright © Edinburgh Mathematical Society 2011

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