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Published May 2010 | Version Submitted
Journal Article Open

The Hilbert transform of a measure

Creators

  • 1. ROR icon Texas A&M University
  • 2. ROR icon California Institute of Technology

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

Identifiers

Eprint ID
21947
DOI
10.1007/s11854-010-0017-0
Resolver ID
CaltechAUTHORS:20110201-094527717

Related works

Describes
10.1007/s11854-010-0017-0 (DOI)
https://arxiv.org/abs/0811.0791 (URL)

Funding

NSF
DMS-0800300
NSF
DMS-0652919
NSF
DMS-0965411

Dates

Created
2011-02-14
Created from EPrint's datestamp field
Updated
2021-11-09
Created from EPrint's last_modified field

Caltech Custom Metadata

Caltech groups
Mathematics Department , Physics Department