Modular inequalities for averaging-type operators

Let (N, nu) be a probability measure space, and, for almost every theta eps ilon N, let T-theta be a sublinear operator of weak type (1, 1) and bounded in L-infinity both with norm less than or equal to 1. The purpose of this work is to study modular inequalities for operators of the form (C) 2001 Ac ademic Press.