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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Norms on earthquake measures and Zygmund functions


Author: Jun Hu
Journal: Proc. Amer. Math. Soc. 133 (2005), 193-202
MSC (2000): Primary 37E10; Secondary 37F30
Published electronically: June 23, 2004
MathSciNet review: 2085170
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Abstract: The infinitesimal earthquake theorem gives a one-to-one correspondence between Thurston bounded earthquake measures and normalized Zygmund bounded functions. In this paper, we provide an intrinsic proof of a theorem given in an earlier paper by the author; that is, we show that the cross-ratio norm of a Zygmund bounded function is equivalent to the Thurston norm of the earthquake measure in the correspondence.


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Additional Information

Jun Hu
Affiliation: Department of Mathematics, Brooklyn College, CUNY, Brooklyn, New York 11210
Email: jun@sci.brooklyn.cuny.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07545-8
PII: S 0002-9939(04)07545-8
Keywords: Earthquake measures, Zygmund functions
Received by editor(s): March 14, 2003
Received by editor(s) in revised form: September 19, 2003
Published electronically: June 23, 2004
Additional Notes: This work was supported in part by an NSF postdoctoral research fellowship (DMS 9804393), an Incentive Scholar Fellowship of The City University of New York (2000-01) and PSC-CUNY research grants.
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2004 American Mathematical Society