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

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 weight...

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Bibliographic Details
Published in:arXiv.org 2011-03
Main Authors: Hytönen, Tuomas P, Lacey, Michael T, Reguera, Maria Carmen, Vagharshakyan, Armen
Format: Article
Language:English
Subjects:
Hilbert transformation
Inequalities
Operators
Online Access:Get full text
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Summary: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
ISSN:2331-8422