Weighted estimates for one-sided martingale transforms

Document Type

Article

Publication Date

1-1-2020

Abstract

Let Tf = ΣI ϵI {f, hI+}hI-. Here, |ϵI | = 1, and hJ is the Haar function defined on dyadic interval J. We show that, for instance, (Equation Presented) Above, we use the one-sided A2 characteristic for the weight w. This is an instance of a one-sided A2 conjecture. Our proof of this fact is difficult, as the very quick known proofs of the A2 theorem do not seem to apply in the one-sided setting.

Publication Source (Journal or Book title)

Proceedings of the American Mathematical Society

First Page

235

Last Page

245

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