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

It is shown that for every 2-concave Banach lattice $X$ of measurable fuctions on the circle, the quotient space $X/X_A$ has cotype 2. Here $X_A$ 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 $X_A$ factors through $L^p_A=H^p$ and extends to $X$, provided that $X$ is 2-convex.