previous :: next
Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transforms
Rodrigo Bañuelos and Gang Wang
Source: Duke Math. J. Volume 80, Number 3
(1995), 575-600.
First Page:
Show
Hide
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.dmj/1077246287
Mathematical Reviews number (MathSciNet): MR1370109
Zentralblatt MATH identifier: 0853.60040
Digital Object Identifier: doi:10.1215/S0012-7094-95-08020-X
References
[1] K. Astala, Area distortion of quasiconformal mappings, Acta Math. 173 (1994), no. 1, 37–60.
Mathematical Reviews (MathSciNet): MR95m:30028b
Zentralblatt MATH: 0815.30015
Digital Object Identifier: doi:10.1007/BF02392568
[2] Baernstein and J. Manfredi, Topics in quasiconformal mapping, Topics in modern harmonic analysis, Vol. I, II (Turin/Milan, 1982), Ist. Naz. Alta Mat. Francesco Severi, Rome, 1983, pp. 819–862.
Mathematical Reviews (MathSciNet): MR85j:30037
Zentralblatt MATH: 0567.30015
[3] R. Bañuelos, Martingale transforms and related singular integrals, Trans. Amer. Math. Soc. 293 (1986), no. 2, 547–563.
Mathematical Reviews (MathSciNet): MR87h:60095
Zentralblatt MATH: 0591.60045
Digital Object Identifier: doi:10.2307/2000021
[4] R. Bañuelos, A sharp good-$\lambda$ inequality with an application to Riesz transforms, Michigan Math. J. 35 (1988), no. 1, 117–125.
Mathematical Reviews (MathSciNet): MR89c:42023
Zentralblatt MATH: 0662.60057
Digital Object Identifier: doi:10.1307/mmj/1029003685
Project Euclid: euclid.mmj/1029003685
[5] D. L. Burkholder, Boundary value problems and sharp inequalities for martingale transforms, Ann. Probab. 12 (1984), no. 3, 647–702.
Mathematical Reviews (MathSciNet): MR86b:60080
Zentralblatt MATH: 0556.60021
Digital Object Identifier: doi:10.1214/aop/1176993220
Project Euclid: euclid.aop/1176993220
[6] D. L. Burkholder, Sharp inequalities for martingales and stochastic integrals, Astérisque (1988), no. 157-158, 75–94.
Mathematical Reviews (MathSciNet): MR90b:60051
Zentralblatt MATH: 0656.60055
[7] D. L. Burkholder, Explorations in martingale theory and its applications, École d'Été de Probabilités de Saint-Flour XIX—1989, Lecture Notes in Math., vol. 1464, Springer, Berlin, 1991, pp. 1–66.
Mathematical Reviews (MathSciNet): MR92m:60037
Zentralblatt MATH: 0771.60033
[8] R. Durrett, Brownian motion and martingales in analysis, Wadsworth Mathematics Series, Wadsworth International Group, Belmont, CA, 1984.
Mathematical Reviews (MathSciNet): MR87a:60054
Zentralblatt MATH: 0554.60075
[9] M. Essén, A superharmonic proof of the M. Riesz conjugate function theorem, Ark. Mat. 22 (1984), no. 2, 241–249.
Mathematical Reviews (MathSciNet): MR86c:30068
Zentralblatt MATH: 0562.30002
Digital Object Identifier: doi:10.1007/BF02384381
[10] R. F. Gundy and N. Th. Varopoulos, Les transformations de Riesz et les intégrales stochastiques, C. R. Acad. Sci. Paris Sér. A-B 289 (1979), no. 1, A13–A16.
Mathematical Reviews (MathSciNet): MR82e:60089
Zentralblatt MATH: 0413.60003
[11] T. Iwaniec, Extremal inequalities in Sobolev spaces and quasiconformal mappings, Z. Anal. Anwendungen 1 (1982), no. 6, 1–16.
Mathematical Reviews (MathSciNet): MR85g:30027
Zentralblatt MATH: 0577.46038
[12] T. Iwaniec and R. Kosecki, Sharp estimates for complex potentials and quasiconformal mappings, preprint.
[13] T. Iwaniec and G. Martin, Quasiregular mappings in even dimensions, Acta Math. 170 (1993), no. 1, 29–81.
Mathematical Reviews (MathSciNet): MR94m:30046
Zentralblatt MATH: 0785.30008
Digital Object Identifier: doi:10.1007/BF02392454
[14] T. Iwaniec and G. Martin, The Beurling-Ahlfors transform in $\mathbbR^n$ and related singular integrals, preprint.
[15] O. Lehto, Remarks on the integrability of the derivatives of quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. A I No. 371 (1965), 8.
Mathematical Reviews (MathSciNet): MR31:5975
Zentralblatt MATH: 0137.05503
[16] S. K. Pichorides, On the best values of the constants in the theorems of M. Riesz, Zygmund and Kolmogorov, Studia Math. 44 (1972), 165–179. (errata insert).
Mathematical Reviews (MathSciNet): MR47:702
Zentralblatt MATH: 0238.42007
[17] P. Protter, Stochastic integration and differential equations, Applications of Mathematics, vol. 21, Springer-Verlag, Berlin, 1990.
Mathematical Reviews (MathSciNet): MR91i:60148
Zentralblatt MATH: 0694.60047
[18] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, 1979.
Mathematical Reviews (MathSciNet): MR290095
[19] N. Th. Varopoulos, Aspects of probabilistic Littlewood-Paley theory, J. Funct. Anal. 38 (1980), no. 1, 25–60.
Mathematical Reviews (MathSciNet): MR82d:42016
Zentralblatt MATH: 0462.60050
Digital Object Identifier: doi:10.1016/0022-1236(80)90055-5
[20] G. Wang, Differential subordination and strong differential subordination for continuous-time martingales and related sharp inequalities, Ann. Probab. 23 (1995), no. 2, 522–551.
Mathematical Reviews (MathSciNet): MR96b:60120
Zentralblatt MATH: 0832.60055
Digital Object Identifier: doi:10.1214/aop/1176988278
Project Euclid: euclid.aop/1176988278
previous :: next
Duke Mathematical Journal
