## Access

You are not currently logged in.

Access JSTOR through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Journal Article

# Martingale Transforms and Related Singular Integrals

Rodrigo Bañuelos
Transactions of the American Mathematical Society
Vol. 293, No. 2 (Feb., 1986), pp. 547-563
DOI: 10.2307/2000021
Stable URL: http://www.jstor.org/stable/2000021
Page Count: 17
Were these topics helpful?

#### Select the topics that are inaccurate.

Cancel
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available

## Abstract

The operators obtained by taking conditional expectation of continuous time martingale transforms are studied, both on the circle T and on Rn. 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 $L^p(R^n), 1 < p < \infty$, 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 $L^p(R^n), 1 < p < \infty$, with constants independent of n.

• 547
• 548
• 549
• 550
• 551
• 552
• 553
• 554
• 555
• 556
• 557
• 558
• 559
• 560
• 561
• 562
• 563