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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Continuity of weighted estimates in $A_{p}$ norm
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by Nikolaos Pattakos and Alexander Volberg PDF
Proc. Amer. Math. Soc. 140 (2012), 2783-2790 Request permission

Abstract:

We prove that for a general CalderĂłn-Zygmund operator $T$ the numbers $\|T\|_{L^{p}(w)\rightarrow L^{p}(w)}$ converge to $\|T\|_{L^{p}(dx)\rightarrow L^{p}(dx)}$ 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
  • MR Author ID: 960560
  • Email: pattakos@msu.edu
  • Alexander Volberg
  • Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
  • 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
  • © Copyright 2011 American Mathematical Society
  • 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
  • MathSciNet review: 2910765