Noncommutative Khintchine and Paley inequalities via generic factorization

Abstract

We reprove an inequality for Rademacher series with coefficients in the Schatten class $S_1$. Our method yields the same estimate for coefficients after suitable gaps in $S_1$-valued trigonometric series; this was known for scalar-valued functions. A very similar method gives a new proof of the extension to $S_1$-valued $H^1$ functions of Paley's theorem about lacunary coefficients.

Subspaces $M_j$ and $L_j$ are suitably enlarged to fix errors in the first version of this paper. See the last sentence in the new Remark 3.4