Weighted estimates for one-sided martingale transforms

Authors

Wei Chen, Yangzhou University
Rui Han, Georgia Institute of Technology
Michael T. Lacey, Georgia Institute of Technology

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

Recommended Citation

Chen, W., Han, R., & Lacey, M. (2020). Weighted estimates for one-sided martingale transforms. Proceedings of the American Mathematical Society, 148 (1), 235-245. https://doi.org/10.1090/proc/14665