Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Martingale transforms and related singular integrals


Author: Rodrigo Bañuelos
Journal: Trans. Amer. Math. Soc. 293 (1986), 547-563
MSC: Primary 60G44; Secondary 42B20, 60G46, 60H05
DOI: https://doi.org/10.1090/S0002-9947-1986-0816309-0
MathSciNet review: 816309
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The operators obtained by taking conditional expectation of continuous time martingale transforms are studied, both on the circle $ T$ and on $ {{\mathbf{R}}^n}$. Using a Burkholder-Gundy inequality for vector-valued martingales, it is shown that the vector formed by any number of these operators is bounded on $ {L^p}({{\mathbf{R}}^n}),\,1 < p < \infty $, with constants that depend only on $ p$ and the norms of the matrices involved. As a corollary we obtain a recent result of Stein on the boundedness of the Riesz transforms on $ {L^p}({{\mathbf{R}}^n}),\,1 < p < \infty $, with constants independent of $ n$.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60G44, 42B20, 60G46, 60H05

Retrieve articles in all journals with MSC: 60G44, 42B20, 60G46, 60H05


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1986-0816309-0
Article copyright: © Copyright 1986 American Mathematical Society