This is an announcement for the paper "Sharp weighted estimates for classical operators" by David Cruz-Uribe, Jose Maria Martell, and Carlos Perez.
Abstract: We give a new proof of the sharp one weight $L^p$ inequality for any operator $T$ that can be approximated by Haar shift operators such as the Hilbert transform, any Riesz transform, the Beurling-Ahlfors operator. Our proof avoids the Bellman function technique and two weight norm inequalities. We use instead a recent result due to A. Lerner to estimate the oscillation of dyadic operators. Our method is flexible enough to prove the corresponding sharp one-weight norm inequalities for some operators of harmonic analysis: the maximal singular integrals associated to $T$, Dyadic square functions and paraproducts, and the vector-valued maximal operator of C. Fefferman-Stein. Also we can derive a very sharp two-weight bump type condition for $T$.
Archive classification: math.CA math.FA
Mathematics Subject Classification: 42B20; 42B25
The source file(s), dyadic-hilbert.tex: 72598 bytes, is(are) stored in gzipped form as 1001.4254.gz with size 21kb. The corresponding postcript file has gzipped size 84kb.
Submitted from: carlosperez@us.es
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