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Dyadic Fefferman–Stein inequalities and the equivalence of Haar bases on weighted Lebesgue spaces

Published online by Cambridge University Press:  11 February 2011

Hugo Aimar ,
Ana Bernardis  and
Luis Nowak
Hugo Aimar
Affiliation:
Departamento de Matemática (FIQ-UNL), Santiago del Estero 2829 (3000) Santa Fe, Argentina and IMAL-CONICET, Güemes 3450 (3000) Santa Fe, Argentina ([email protected]; [email protected])
Ana Bernardis
Affiliation:
Departamento de Matemática (FIQ-UNL), Santiago del Estero 2829 (3000) Santa Fe, Argentina and IMAL-CONICET, Güemes 3450 (3000) Santa Fe, Argentina ([email protected]; [email protected])
Luis Nowak
Affiliation:
Departamento de Matemática (FaEA-UNComa), Buenos Aires 1400 (8300), Neuquén, Argentina and IMAL-CONICET, Güemes 3450 (3000) Santa Fe, Argentina ([email protected])
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Abstract

We give sufficient conditions on two dyadic systems to obtain the equivalence of corresponding Haar systems on dyadic weighted Lebesgue spaces on spaces of homogeneous type. In order to obtain these results, we prove a Fefferman–Stein weighted inequality for vector-valued dyadic Hardy–Littlewood maximal operators with dyadic weights in this general setting.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 1 , February 2011 , pp. 1 - 22
Copyright
Copyright © Royal Society of Edinburgh 2011

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