Geometric-arithmetic averaging of dyadic weights

الأصل · EN

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 Aₚ weights from a measurably varying family of dyadic Aₚ weights. This averaging process is suggested by the relationship between the Aₚ weight class and the space of functions of bounded mean oscillation. The same averaging process also constructs weights satisfying reverse Holder (RHₚ) conditions from families of dyadic RHₚ weights, and extends to the polydisc as well.