A sharp estimate of weighted dyadic shifts of complexity 0 and 1

Abstract

A simple shortcut to proving sharp weighted estimates for the Martingale Transform and for the dyadic shift of order 1 (and so for the Hilbert transform) is presented. It is a unified proof for these both transforms. Key words: Calder\on--Zygmund operators, $A_2$ weights, $A_1$ weights, Carleson embedding theorem, Bellman function, dyadic shifts, nonhomogeneous Harmonic Analysis.

arXiv comment8 pages

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Cited by in corpus (4)

• Sharp $A_2$ estimates of Haar shifts via Bellman function
• On the A_2 inequality for Calderon-Zygmund Operators
• A linear dimensionless bound for the weighted Riesz vector
• Analysis of the Ahlfors-Beurling operator (lecture notes for the summer school at the University of Seville, 2013)