Sharp Estimate of the Ahlfors-Beurling Operator via Averaging Martingale Transforms

Michigan Mathematical Journal

Volumn 51, Issue 2, 2003, Pages 415-435

  Dragičević, Oliver ^a   Volberg, Alexander ^a  

^a MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17044444969     PISSN: 00262285     EISSN: None     Source Type: Journal    
DOI: 10.1307/mmj/1060013205     Document Type: Article

References (9)

1. K. Astala, T. Iwaniec, and E. Saksman, Beltrami operators in the plane, Duke Math. J. 107 (2001), 27-56.
2. R. Bañuelos and P. J. Méndez-Hernández, Space-time Brownian motion and the Beurling-Ahlfors transform, Indiana Univ. Math. J. (to appear).
3. R. Bañuelos and G. Wang, Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transforms, Duke Math. J. 80 (1995), 575-600.
4. T. Iwaniec, Extremal inequalities in Sobolev spaces and quasiconformal mappings, Z. Anal. Anwendungen 1 (1982), 1-16.
5. F. Nazarov and A. Volberg, Heating of the Ahlfors-Beurling operator and the estimates of its norms, St. Petersburg Math. J. (to appear).
6. S. Petermichl, S. Treil, and A. Volberg, Why the Riesz transforms are averages of the dyadic shifts, Proceedings of the 6th harmonic analysis conference (El Escorial), Publ. Mat. (to appear).
7. S. Petermichl and A. Volberg, Heating of the Ahlfors-Beurling operator: Weakly quasiregular maps on the plane are quasiregular, Duke Math. J. 112 (2002), 281-305.
8. W. Rudin, Functional analysis, McGraw-Hill, New York, 1991.
9. J. Wittwer, A sharp estimate on the norm of the martingale transform, Math. Res. Lett. 7 (2000), 1-12.