Strong factorization of operators defined on subspaces of analytic functions in lattices

Abstract

It is shown that for every 2-concave Banach lattice X of measurable fuctions on the circle, the quotient space X/XA has cotype 2. Here XA denotes the subclass of X consisting of the boundary values of analytic functions. It is also shown that, under slight additional assumptions, a p-concave operator defined on XA factors through L A p = Hp and extends to X, provided that X is p-convex. Bibliography: 10 titles.