Quantitative affine approximation for UMD targets

Tuomas Hytönen, Sean Li, Assaf Naor

It is shown here that if $(Y,\Vert \cdot {\Vert }_Y)$ is a Banach space in which martingale differences are unconditional (a UMD Banach space) then there exists $c=c(Y)\in (0,\infty )$ with th…