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

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

2011-04-28

arxiv.org/abs/1104.5347v1

Mathematics

Classical Analysis and ODEs

8 pages

Scientific paper

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.

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