Mathematische Zeitschrift

, Volume 282, Issue 3–4, pp 955–972 | Cite as

On the \(A_{\infty }\) conditions for general bases

  • Javier DuoandikoetxeaEmail author
  • Francisco J. Martín-Reyes
  • Sheldy Ombrosi


We discuss several characterizations of the \(A_\infty \) class of weights in the setting of general bases. Although they are equivalent for the usual Muckenhoupt weights, we show that they can give rise to different classes of weights for other bases. We also obtain new characterizations for the usual \(A_\infty \) weights.


Weights Muckenhoupt bases \(A_p\) Classes 

Mathematics Subject Classification

Primary 42B25 



We would like to thank David Cruz-Uribe for calling to our attention reference [31] and the characterizations with the medians appearing in it. We thank also Amiran Gogatishvili for pointing out his paper [16] and Kabe Moen for indicating the recent characterization of [19].


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Javier Duoandikoetxea
    • 1
    Email author
  • Francisco J. Martín-Reyes
    • 2
  • Sheldy Ombrosi
    • 3
  1. 1.Departamento de MatemáticasUniversidad del País Vasco/Euskal Herriko Unibertsitatea (UPV/EHU)BilbaoSpain
  2. 2.Departamento de Análisis Matemático, Facultad de CienciasUniversidad de MálagaMálagaSpain
  3. 3.Departamento de MatemáticaUniversidad Nacional del SurBahía BlancaArgentina

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