On connections between delta-convex mappings and convex operators

We study conditions under which every delta-convex (d.c.) mapping is the difference of two continuous convex operators, and vice versa. In particular, we prove that each d.c. mapping F : (a, b) -> Y is the difference of two continuous convex operators whenever Y belongs to a large class of Banach lattices which includes all L-p (mu) spaces (1 <= p <= infinity). The proof is based on a result about Jordan decomposition of vector-valued functions. New observations on Jordan decomposition of finitely additive vector-valued measures are also presented.