The sharp A(p) constant for weights in a reverse-Holder class

Martin Dindos, Treven Wall

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Coifman and Fefferman established that the class of Muckenhoupt weights is equivalent to the class of weights satisfying the "reverse Holder inequality". In a recent paper V. Vasyunin [17] presented a proof of the reverse Holder inequality with sharp constants for the weights satisfying the usual Muckenhoupt condition. In this paper we present the inverse, that is, we use the Bellman function technique to find the sharp A(p) constants for weights in a reverse-Holder class on an interval; we also find the sharp constants for the higher-integrability result of Gehring [7].

Additionally, we find sharp bounds for the A(p) constants of reverse-Holder-class weights defined on rectangles in R-n, as well as bounds on the A(p) constants for reverse-Holder weights defined on cubes in R-n, without claiming the sharpness.

Original languageEnglish
Pages (from-to)559-594
Number of pages36
JournalRevista matematica iberoamericana
Issue number2
Publication statusPublished - 2009


  • Reverse-Holder class
  • Gehring class
  • A(p) weight
  • Muckenhoupt weight
  • Bellman function

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