Third-Year Requirement: Weighted Estimates for the Martingale Transform and One-Sided Calderón-Zygmund Operators

Abstract: We prove sharp weighted bounds for the martingale transform using the disbalanced Haar functions. Our proof of the Bilinear Embedding Theorem relies on the Carleson Lemma, which results in a single condition that needs to be checked before applying the Bilinear Theorem. We examine the limitations of this method when applied to the one-sided martingale transform and explore the proof of its boundedness using testing conditions. We finally discuss how the $A_p^+$ weights determine the boundedness of one-sided Calderón-Zygmund operators.

*Please note the location change to Crow Hall, Room 205 for this Analysis Seminar.