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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.

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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.

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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.
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Issue or Number:1
Record Number:CaltechAUTHORS:20110201-094527717
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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
Deposited By: Tony Diaz
Deposited On:14 Feb 2011 17:43
Last Modified:03 Oct 2019 02:32

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