Sharp weighted norm inequalities for Littlewood–Paley operators and singular integrals |
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Authors: | Andrei K Lerner |
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Institution: | Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel |
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Abstract: | 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<∞. |
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Keywords: | MSC: 42B20 42B25 |
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