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The Hilbert transform of a measure

Poltoratski, Alexei and Simon, Barry and Zinchenko, Maxim (2010) The Hilbert transform of a measure. Journal d'Analyse Mathématique, 111 (1). pp. 247-265. ISSN 0021-7670. https://resolver.caltech.edu/CaltechAUTHORS:20110201-094527717

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Abstract

Let e be a homogeneous subset of R in the sense of Carleson. Let μ be a finite positive measure on R and H_μ(x) its Hilbert transform. We prove that if lim_(t→∞)t|e∩{x||H_μ(x)|>t}| = 0, then μ_s(e) = 0, where μ_s is the singular part of μ.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s11854-010-0017-0 DOIArticle
http://www.springerlink.com/content/3351607304360466/PublisherArticle
https://arxiv.org/abs/0811.0791arXivDiscussion Paper
http://rdcu.be/rIAdPublisherFree ReadCube access
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:© 2010 Springer. Received December 9, 2008. Supported in part by NSF grant DMS-0800300; Supported in part by NSF grant DMS-0652919; Supported in part by NSF grant DMS-0965411.
Funders:
Funding AgencyGrant Number
NSFDMS-0800300
NSFDMS-0652919
NSFDMS-0965411
Issue or Number:1
Record Number:CaltechAUTHORS:20110201-094527717
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20110201-094527717
Official Citation:Poltoratski, A., Simon, B. & Zinchenko, M. JAMA (2010) 111: 247. doi:10.1007/s11854-010-0017-0
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:21947
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:14 Feb 2011 17:43
Last Modified:03 Oct 2019 02:32

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