Illinois Journal of Mathematics

Operator-valued martingale transforms and R-boundedness

Abstract

Banach space $X$-valued martingale transforms by a $\mathcal{B}(X)$-valued multiplier sequence are bounded on $L_p(X)$, where $1<p<\infty$ and $X$ is a UMD space, if and only if the multiplier sequence is pointwise R-bounded. This is also true for unconditionally convergent martingales in arbitrary Banach spaces.

Article information

Source
Illinois J. Math., Volume 49, Number 2 (2005), 487-516.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138030

Digital Object Identifier
doi:10.1215/ijm/1258138030

Mathematical Reviews number (MathSciNet)
MR2164348

Zentralblatt MATH identifier
1080.60042

Citation

Girardi, Maria; Weis, Lutz. Operator-valued martingale transforms and R-boundedness. Illinois J. Math. 49 (2005), no. 2, 487--516. doi:10.1215/ijm/1258138030. https://projecteuclid.org/euclid.ijm/1258138030