JournalsrmiVol. 27, No. 3pp. 953–976

Geometric-arithmetic averaging of dyadic weights

  • Jill Pipher

    Brown University, Providence, USA
  • Lesley A. Ward

    University of South Australia, Mawson Lakes, Australia
  • Xiao Xiao

    Brown University, Providence, USA
Geometric-arithmetic averaging of dyadic weights cover
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Abstract

The theory of Muckenhoupt's weight functions arises in many areas of analysis, for example in connection with bounds for singular integrals and maximal functions on weighted spaces. We prove that a certain averaging process gives a method for constructing ApA_p weights from a measurably varying family of dyadic ApA_p weights. This averaging process is suggested by the relationship between the ApA_p weight class and the space of functions of bounded mean oscillation. The same averaging process also constructs weights satisfying reverse Hölder (RHpRH_p) conditions from families of dyadic RHpRH_p weights, and extends to the polydisc as well.

Cite this article

Jill Pipher, Lesley A. Ward, Xiao Xiao, Geometric-arithmetic averaging of dyadic weights. Rev. Mat. Iberoam. 27 (2011), no. 3, pp. 953–976

DOI 10.4171/RMI/659