Weighted estimates for powers of the Ahlfors-Beurling operator

Author:
Oliver Dragičević

Journal:
Proc. Amer. Math. Soc. **139** (2011), 2113-2120

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 Ahlfors-Beurling 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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Additional Information

**Oliver Dragičević**

Affiliation:
Faculty of Mathematics and Physics and Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

Email:
oliver.dragicevic@fmf.uni-lj.si

DOI:
https://doi.org/10.1090/S0002-9939-2010-10645-7

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. P1-0291).

Communicated by:
Franc Forstneric

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.