Published May 2010
| Submitted
Journal Article
Open
The Hilbert transform of a measure
Chicago
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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.
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.Attached Files
Submitted - 0811.0791
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Additional details
- Eprint ID
- 21947
- DOI
- 10.1007/s11854-010-0017-0
- Resolver ID
- CaltechAUTHORS:20110201-094527717
- NSF
- DMS-0800300
- NSF
- DMS-0652919
- NSF
- DMS-0965411
- Created
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2011-02-14Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field