Weighted estimates for powers of the AhlforsBeurling operator
Author:
Oliver Dragičević
Journal:
Proc. Amer. Math. Soc. 139 (2011), 21132120
MSC (2010):
Primary 42B20; Secondary 47A10
Published electronically:
November 15, 2010
MathSciNet review:
2775389
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Abstract: We prove that for any , and any weight from the Muckenhoupt class, the norm of the th power of the AhlforsBeurling operator on the weighted Lebesgue space is majorized by , where is the characteristic of . We apply this estimate for a result concerning the spectrum of on .
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 J. Wittwer: A sharp estimate on the norm of the martingale transform, Math. Res. Lett. 7 (2000), no. 1, 112. MR 1748283 (2001e:42022)
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Additional Information
Oliver Dragičević
Affiliation:
Faculty of Mathematics and Physics and Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, SI1000 Ljubljana, Slovenia
Email:
oliver.dragicevic@fmf.unilj.si
DOI:
http://dx.doi.org/10.1090/S000299392010106457
Received by editor(s):
February 10, 2010
Received by editor(s) in revised form:
June 5, 2010
Published electronically:
November 15, 2010
Additional Notes:
This work was partially supported by the Ministry of Higher Education, Science and Technology of Slovenia (research program Analysis and Geometry, contract no. P10291).
Communicated by:
Franc Forstneric
Article copyright:
© Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
