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 weights from a measurably varying family of dyadic weights. This averaging process is suggested by the relationship between the weight class and the space of functions of bounded mean oscillation. The same averaging process also constructs weights satisfying reverse Hölder () conditions from families of dyadic 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. 953–976DOI 10.4171/RMI/659