Weak and Strong-type estimates for Haar Shift Operators: Sharp power on the $A_p$ characteristic

Details Weak and Strong-type estimates for Haar Shift Operators: Sharp power on the $A_p$ characteristic Weak and Strong-type estimates for Haar Shift Operators: Sharp power on the $A_p$ characteristic

2009-11-03

arxiv.org/abs/0911.0713v2

Mathematics

Classical Analysis and ODEs

The paper has been withdrawn by the authors. The main results of this paper are improved and extended in arXiv:1103.5229. Also

Scientific paper

As a corollary to our main result we deduce sharp A_p$ inequalities for T being either the Hilbert transform in dimension d=1, the Beurling transform in dimension d=2, or a Riesz transform in any dimension d\ge 2. For T_{\ast} the maximal truncations of these operators, we prove the sharp A_p weighted weak and strong-type L ^{p} (w) inequalities, for all 1

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