On the weak-type constant of the Beurling-Ahlfors transform
Rodrigo Bañuelos and Prabhu Janakiraman
Source: Michigan Math. J. Volume 58, Issue 2 (2009), 459-477.
Primary Subjects: 42, 44
Secondary Subjects: 30, 46
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.mmj/1250169072
Digital Object Identifier: doi:10.1307/mmj/1250169072
References
K. Astala, Area distortion of quasiconformal mappings, Acta Math. 173 (1994), 37--60.
Mathematical Reviews (MathSciNet):
MR1294669
Zentralblatt MATH:
0815.30015
Digital Object Identifier: doi:10.1007/BF02392568
A. Baernstein II and S. Montgomery-Smith, Some conjectures about integral means of $\partial f$ and $\bar\partial f,$ Complex analysis and differential equations (Uppsala, 1997), Acta Univ. Upsaliensis Skr. Uppsala Univ. C Organ. Hist., 64, pp. 92--109, Uppsala Univ., Uppsala, 1999.
Mathematical Reviews (MathSciNet):
MR1758918
Zentralblatt MATH:
0966.30001
R. Bañuelos and P. Janakiraman, $L^p$-bounds for the Beurling--Ahlfors transform, Trans. Amer. Math. Soc. 360 (2008), 3603--3612.
Mathematical Reviews (MathSciNet):
MR2386238
Zentralblatt MATH:
05294133
Digital Object Identifier: doi:10.1090/S0002-9947-08-04537-6
R. Bañuelos and P. Méndez-Hernández, Space-time Brownian motion and the Beurling--Ahlfors transform, Indiana Univ. Math. J. 52 (2003), 981--990.
Mathematical Reviews (MathSciNet):
MR2001941
Zentralblatt MATH:
1080.60043
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.
Mathematical Reviews (MathSciNet):
MR1370109
Zentralblatt MATH:
0853.60040
Digital Object Identifier: doi:10.1215/S0012-7094-95-08020-X
Project Euclid: euclid.dmj/1077246287
D. L. Burkholder, Boundary value problems and sharp inequalities for Martingale transforms, Ann. Probab. 12 (1984), 647--702.
Mathematical Reviews (MathSciNet):
MR744226
Zentralblatt MATH:
0556.60021
Digital Object Identifier: doi:10.1214/aop/1176993220
Project Euclid: euclid.aop/1176993220
------, Sharp inequalities for martingales and stochastic integrals, Colloque Paul Lévy sur les processus stochastiques (Palaiseau, 1987), Astérisque 157--158 (1988), 75--94.
Mathematical Reviews (MathSciNet):
MR976214
Zentralblatt MATH:
0656.60055
------, Martingales and singular integrals in Banach spaces, Handbook of the geometry of Banach spaces (W. B. Johnson, J. Lindenstrauss, eds.), vol. 1, pp. 233--269, Elsevier, Amsterdam, 2001.
Mathematical Reviews (MathSciNet):
MR1863694
Zentralblatt MATH:
1029.46007
Digital Object Identifier: doi:10.1016/S1874-5849(01)80008-5
S. Donaldson and D. Sullivan, Quasiconformal 4-manifolds, Acta Math. 163 (1989), 181--252.
Mathematical Reviews (MathSciNet):
MR1032074
Zentralblatt MATH:
0704.57008
Digital Object Identifier: doi:10.1007/BF02392736
O. Dragičević and A. Volberg, Bellman functions, Littlewood--Paley estimates and asymptotics for the Ahlfors--Beurling operator in $L^p(\Bbb C),$ Indiana Univ. Math. J. 54 (2005), 971--995.
Mathematical Reviews (MathSciNet):
MR2164413
Zentralblatt MATH:
1103.47036
Digital Object Identifier: doi:10.1512/iumj.2005.54.2554
G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge Univ. Press, Cambridge, 1934.
T. Iwaniec, Extremal inequalities in Sobolev spaces and quasiconformal mappings, Z. Anal. Anwendungen 1 (1982), 1--16.
Mathematical Reviews (MathSciNet):
MR719167
------, The best constant in a BMO-inequality for the Beurling--Ahlfors transform, Michigan Math. J. 33 (1986), 387--394.
Mathematical Reviews (MathSciNet):
MR856530
Digital Object Identifier: doi:10.1307/mmj/1029003418
Project Euclid: euclid.mmj/1029003418
------, $L^p$-theory of quasiregular mappings. Quasiconformal space mappings, Lecture Notes in Math., 1508, Springer-Verlag, Berlin, 1992.
Mathematical Reviews (MathSciNet):
MR1187085
T. Iwaniec and G. Martin, Quasiregular mappings in even dimensions, Acta Math. 170 (1993), 29--81.
Mathematical Reviews (MathSciNet):
MR1208562
Zentralblatt MATH:
0785.30008
Digital Object Identifier: doi:10.1007/BF02392454
O. Lehto, Remarks on the integrability of the derivatives of quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. A I Math. 371 (1965), 3--8.
Mathematical Reviews (MathSciNet):
MR181748
F. Nazarov and A. Volberg, Heat extension of the Beurling operator and estimates for its norm, St. Petersburg Math. J. 15 (2004), 563--573.
Mathematical Reviews (MathSciNet):
MR2068982
B. G. Pachpatte, Mathematical inequalities, North-Holland Math. Library, 67, Elsevier, Amsterdam, 2005.
Mathematical Reviews (MathSciNet):
MR2147066
Zentralblatt MATH:
1091.26008
The Michigan Mathematical Journal
