Factoring functions of Maurey's factorization theorem (Q1097470)

The purpose of the paper is to prove that the best possible factoring functions in Maurey's factorization theorem are unique up to multiplication by constant modular functions. The proof is made by treating a certain extremal problem in an L 2-space: Let T be a bounded closed convex set in L s(\(\mu)\), \(0<s<1\). If T consists of nonnegative functions, then T admits a unique function g whose quasi-norm is maximum in T and such that \[ \int (f-g)g^{s-1}d\mu \leq 0,\quad \forall f\in T. \] The reverse conclusion holds in the case \(1<s<+\infty\), which is due to the referee.