Duke Mathematical Journal

Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transforms

Rodrigo Bañuelos and Gang Wang

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Article information

Source
Duke Math. J., Volume 80, Number 3 (1995), 575-600.

Dates
First available in Project Euclid: 19 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077246287

Digital Object Identifier
doi:10.1215/S0012-7094-95-08020-X

Mathematical Reviews number (MathSciNet)
MR1370109

Zentralblatt MATH identifier
0853.60040

Subjects
Primary: 60G44: Martingales with continuous parameter
Secondary: 30C80: Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination 60G46: Martingales and classical analysis

Citation

Bañuelos, Rodrigo; Wang, Gang. Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transforms. Duke Math. J. 80 (1995), no. 3, 575--600. doi:10.1215/S0012-7094-95-08020-X. https://projecteuclid.org/euclid.dmj/1077246287


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References

  • [1] K. Astala, Area distortion of quasiconformal mappings, Acta Math. 173 (1994), no. 1, 37–60.
  • [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.
  • [3] R. Bañuelos, Martingale transforms and related singular integrals, Trans. Amer. Math. Soc. 293 (1986), no. 2, 547–563.
  • [4] R. Bañuelos, A sharp good-$\lambda$ inequality with an application to Riesz transforms, Michigan Math. J. 35 (1988), no. 1, 117–125.
  • [5] D. L. Burkholder, Boundary value problems and sharp inequalities for martingale transforms, Ann. Probab. 12 (1984), no. 3, 647–702.
  • [6] D. L. Burkholder, Sharp inequalities for martingales and stochastic integrals, Astérisque (1988), no. 157-158, 75–94.
  • [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.
  • [8] R. Durrett, Brownian motion and martingales in analysis, Wadsworth Mathematics Series, Wadsworth International Group, Belmont, CA, 1984.
  • [9] M. Essén, A superharmonic proof of the M. Riesz conjugate function theorem, Ark. Mat. 22 (1984), no. 2, 241–249.
  • [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.
  • [11] T. Iwaniec, Extremal inequalities in Sobolev spaces and quasiconformal mappings, Z. Anal. Anwendungen 1 (1982), no. 6, 1–16.
  • [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.
  • [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.
  • [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).
  • [17] P. Protter, Stochastic integration and differential equations, Applications of Mathematics, vol. 21, Springer-Verlag, Berlin, 1990.
  • [18] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, 1979.
  • [19] N. Th. Varopoulos, Aspects of probabilistic Littlewood-Paley theory, J. Funct. Anal. 38 (1980), no. 1, 25–60.
  • [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.