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Continuity of weighted estimates in $ A_{p}$ norm


Authors: Nikolaos Pattakos and Alexander Volberg
Journal: Proc. Amer. Math. Soc. 140 (2012), 2783-2790
MSC (2010): Primary 30E20, 47B37, 47B40, 30D55
DOI: https://doi.org/10.1090/S0002-9939-2011-11165-1
Published electronically: December 13, 2011
MathSciNet review: 2910765
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that for a general Calderón-Zygmund operator $ T$ the numbers $ \Vert T\Vert _{L^{p}(w)\rightarrow L^{p}(w)}$ converge to $ \Vert T\Vert _{L^{p}(dx)\rightarrow L^{p}(dx)}$ as the $ A_{p}$ norm of $ w$ converges to $ 1$, i.e. as $ [w]_{A_{p}}\rightarrow 1^{+}$ for $ 1<p<\infty $.


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Additional Information

Nikolaos Pattakos
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: pattakos@msu.edu

Alexander Volberg
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824

DOI: https://doi.org/10.1090/S0002-9939-2011-11165-1
Keywords: Calderón-Zygmund operators, $A_{2}$ weights, interpolation
Received by editor(s): December 1, 2010
Received by editor(s) in revised form: March 7, 2011
Published electronically: December 13, 2011
Communicated by: Mario Bonk
Article copyright: © Copyright 2011 American Mathematical Society

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