Weighted estimates for powers of the Ahlfors-Beurling operator
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- by Oliver Dragičević PDF
- Proc. Amer. Math. Soc. 139 (2011), 2113-2120 Request permission
Abstract:
We prove that for any $n\in \mathbb {Z}\backslash \{0\}$, $p>1$ and any weight $w$ from the Muckenhoupt $A_p$ class, the norm of the $n$-th power of the Ahlfors-Beurling operator $T$ on the weighted Lebesgue space $L^p(w)$ is majorized by $C(p) |n|^3 [w]_p^{\operatorname {max}\{1,1/(p-1)\}}$, where $[w]_p$ is the $A_p$ characteristic of $w$. We apply this estimate for a result concerning the spectrum of $T$ on $L^p(w)$.References
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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
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2113-2120
- MSC (2010): Primary 42B20; Secondary 47A10
- DOI: https://doi.org/10.1090/S0002-9939-2010-10645-7
- MathSciNet review: 2775389