Rademacher series and decoupling

摘要

We study decoupling in quasi-Banach spaces. Weshow that decoupling is permissible in some quasi-Banach spaces(e.g., Lp and Lp/Hp when 0p1) but fails in other spacessuch as the Schatten ideal Sp when 0p1. We alsorelate our ideas to a possible extension of the Grothendieckinequality.