Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Paraproducts and commutators of martingale transforms


Authors: Rodrigo Bañuelos and Andrew G. Bennett
Journal: Proc. Amer. Math. Soc. 103 (1988), 1226-1234
MSC: Primary 60G46; Secondary 60G44
DOI: https://doi.org/10.1090/S0002-9939-1988-0955015-6
MathSciNet review: 955015
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We define paraproducts in a probabilistic setting and study their boundedness properties. As an application of paraproduct techniques, we prove a generalization of the commutator result of Coifman-Rochberg-Weiss [6].


References [Enhancements On Off] (What's this?)

  • [1] J. M. Bony, Calcul symbolique et propagation des singularités pour les équations aux derivées partielles nonlinéaries, Ann. Sci. Ecole. Norm. Sup. (4) 14 (1981), 209-246. MR 631751 (84h:35177)
  • [2] D. L. Burkholder, Martingale transforms, Ann. Math. Statist. 37 (1966), 1494-1504. MR 0208647 (34:8456)
  • [3] -, A sharp inequality for martingale transforms, Ann. Probab. 7 (1979), 858-863. MR 542135 (80j:60067)
  • [4] -, Martingales and Fourier analysis in Banach spaces, Probability and Analysis, Varenna, Lecture Notes in Math., vol. 1206, Springer-Verlag, Berlin and New York, 1985.
  • [5] R. Coifman and Y. Meyer, Au-delà des opérateurs pseudo-différentiels, Asterisque 57 (1978). MR 518170 (81b:47061)
  • [6] R. Coifman, R. Rochberg, and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math. 103 (1976), 611-635. MR 0412721 (54:843)
  • [7] R. Durrett, Brownian motion and martingales in analysis, Wadsworth, Belmont, Calif., 1984. MR 750829 (87a:60054)
  • [8] J. Garnett, Bounded analytic functions, Academic Press, New York, 1980. MR 628971 (83g:30037)
  • [9] A. Garsia, Martingale inequalities, Benjamin, New York, 1973. MR 0448538 (56:6844)
  • [10] R. F. Gundy and N. Th. Varopoulos, Les transformations de Riesz et les intégrales stochastiques, C. R. Acad. Sci. Paris Ser. A 289 (1979), 13-16. MR 545671 (82e:60089)
  • [11] N. Th. Varopoulos, Aspects of probabilistic Littlewood-Paley theory, J. Funct. Anal. 38 (1980), 25-60. MR 583240 (82d:42016)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60G46, 60G44

Retrieve articles in all journals with MSC: 60G46, 60G44


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0955015-6
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society