b-weighted dyadic BMO from dyadic BMO and associatedT(b) theorems

Abstract

Given a function b, and using adapted Haar wavelets, we define a BMO-type norm which is dependent on b. In both global and local cases, we find the dependence of the bounds on f BMO by the bounds on the b-weighted BMO norm of f . We show that the dependence is sharp in the global case. Multiscale analysis is used in the local case. We formulate as corollaries global and local dyadic T (b) theorems whose hypotheses include a bound on the b-weighted BMO-norm of T * (1).