Geometric-arithmetic averaging of dyadic weights

Jill Pipher, Lesley Ward, Xiao Xiao
2011 Revista matemática iberoamericana  
The theory of (Muckenhoupt) weights 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 A p weights from a measurably varying family of dyadic A p weights. This averaging process is suggested by the relationship between the A p weight class and the space of functions of bounded mean oscillation. The same averaging process also constructs
more » ... ss also constructs weights satisfying reverse Hölder (RH p ) conditions from families of dyadic RH p weights, and extends to the polydisc as well. * 2008 Mathematics Subject Classification. Primary: 42B35; Secondary: 42B25.
doi:10.4171/rmi/659 fatcat:2ohtv7drorb7pddruwgwoyrbzu