The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. M. Abramowitz and I. A. Stegun. Handbook of mathematical functions with formulas, graphs, and mathematical tables Reprint of the 1972 edition. Dover Publications, Inc., New York. Math. Review 94b:00012
  2. R. Bañuelos and P. J. Méndez-Hernandez. Space-time Brownian motion and the Beurling-Ahlfors transform, Indiana Univ. Math. J. 52 (2003), 981-990. Math. Review 2004h:60067
  3. R. Bañuelos, G. Wang. Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transformations, Duke Math. J. 80 (1995), 575-600. Math. Review 96k:60108
  4. R. Bañuelos, G. Wang. Orthogonal martingales under differential subordination and applications to Riesz transforms, Illinois J. Math. 40 (1996), 678-691. Math. Review 99a:60047
  5. D. L. Burkholder. Boundary value problems and sharp inequalities for martingale transforms, Ann. Probab. 12 (1984), 647-702. Math. Review 86b:60080
  6. D. L. Burkholder. A proof of Pełczyński's conjecture for the Haar system, Studia Math. 91 (1988), 79-83. Math. Review 89j:46026
  7. D. L. Burkholder. Sharp inequalities for martingales and stochastic integrals, Astérisque 157-158 (1988), 75-94. Math. Review 90b:60051
  8. D. L. Burkholder. Explorations in martingale theory and its applications, Ecole d'Été de Probabilités de Saint Flour XIX-1989, Lecture Notes in Mathematics 1464 (1991), 1-66 . Math. Review 92m:60037
  9. B. Davis. On the Lp norms of stochastic integrals and other martingales, Duke Math. J. 43 (1976), 697-704. Math. Review 0418219
  10. C. Dellacherie and P. A. Meyer. Probabilities and Potential B: Theory of martingales North Holland, Amsterdam, 1982. Math. Review 85e:60001
  11. T. W. Gamelin. Uniform algebras and Jensen measures Cambridge University Press, London, 1978. Math. Review 81a:460581
  12. S. Geiss, S. Montgomery-Smith, E. Saksman. On singular integral and martingale transforms, Trans. Amer. Math. Soc. 362 (2010), 553-575. Math. Review number not available.
  13. A. Osekowski. Maximal inequalities for continuous martingales and their differential subordinates Proc. Amer. Math. Soc. 139 (2011), 721-734. Math. Review number not available.
  14. 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. Math. Review 0312140
  15. D. Revuz and M. Yor. Continuous martingales and Brownian Motion 3rd edition, Springer-Verlag, Berlin, 1999. Math. Review 2000h:60050
  16. G. Wang, Differential subordination and strong differential subordination for continuous time martingales and related sharp inequalities, Ann. Probab. 23 (1995), 522-551. Math. Review 96b:60120
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.