Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: December 13, 2011
Full-text PDF

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 $.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 30E20, 47B37, 47B40, 30D55

Retrieve articles in all journals with MSC (2010): 30E20, 47B37, 47B40, 30D55


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: http://dx.doi.org/10.1090/S0002-9939-2011-11165-1
PII: S 0002-9939(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