A Class of Operators on the Lorentz Space M(ϕ)

Abstract

In order to deal with certain problems in the theory of interpolation spaces, it is convenient to consider operators of the following form:Let k be a non-negative measurable function on the half-line R+, and let ƒ be a measurable function on R+ with1Then the operator T is defined by2with the domain of T, D(T), consisting of all ƒ which satisfy (1).