Sharp weighted norm inequalities for Littlewood–Paley operators and singular integrals
نویسندگان
چکیده
We prove sharp Lp(w) norm inequalities for the intrinsic square function (introduced recently by M. Wilson) in terms of the Ap characteristic of w for all 1 < p <∞. This implies the same sharp inequalities for the classical Lusin area integral S(f ), the Littlewood–Paley g-function, and their continuous analogs Sψ and gψ . Also, as a corollary, we obtain sharp weighted inequalities for any convolution Calderón–Zygmund operator for all 1 <p 3/2 and 3 p <∞, and for its maximal truncations for 3 p <∞. © 2010 Elsevier Inc. All rights reserved. MSC: 42B20; 42B25
منابع مشابه
On Some Weighted Norm Inequalities for Littlewood–paley Operators
It is shown that the Lw,1< p<∞, operator norms of Littlewood–Paley operators are bounded by a multiple of ‖w‖ Ap , where γp = max{1, p/2} 1 p−1 . This improves previously known bounds for all p > 2. As a corollary, a new estimate in terms of ‖w‖Ap is obtained for the class of Calderón–Zygmund singular integrals commuting with dilations.
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Given a weight , we consider the space ML which coincides with L p when ∈ Ap . Sharp weighted norm inequalities on ML for the Calderón–Zygmund and Littlewood–Paley operators are obtained in terms of the Ap characteristic of for any 1<p<∞. © 2005 Elsevier Inc. All rights reserved.
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