A Simple Proof of the Sharp Weighted Estimate for Calderón–Zygmund Operators on Homogeneous Spaces

Here we show that Lerner’s method of local mean oscillation gives a simple proof of the A ₂ conjecture for spaces of homogeneous type, that is, the linear dependence on the A ₂ norm for weighted L ² Calderón–Zygmund operator estimates. In the Euclidean case, the result is due to Hytönen, and for geometrically doubling spaces, Nazarov, Reznikov, and Volberg obtained the linear bound.