A sharp form of the Marcinkiewicz interpolation theorem for Orlicz spaces

摘要

Let (X, mu) and (Y, nu) be sigma-finite measure spaces with mu(X) = nu(Y) = infinity and (Y, nu) nonatomic and separable. Suppose T is a so-called r-quasilinear operator mapping the simple functions on X into the measurable functions on Y that satisfies the weak type conditions