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.

8 pages

References in corpus (3)

• Two weight estimate for the Hilbert transform and corona decomposition for non-doubling measures
• The sharp weighted bound for general Calderon-Zygmund operators
• Current-phase relation of graphene Josephson junctions

Cited by in corpus (2)

• Sharp $A_2$ estimates of Haar shifts via Bellman function
• Analysis of the Ahlfors-Beurling operator (lecture notes for the summer school at the University of Seville, 2013)