On the dual of Cesàro function space

Abstract The goal of this paper is to present an isometric representation of the dual space to Cesaro function space C p , w , 1 p ∞ , induced by arbitrary positive weight function w on interval ( 0 , l ) where 0 l ⩽ ∞ . For this purpose given a strictly decreasing nonnegative function Ψ on ( 0 , l ) , the notion of essential Ψ -concave majorant f ˆ of a measurable function f is introduced and investigated. As applications it is shown that every slice of the unit ball of the Cesaro function space has diameter 2. Consequently, Cesaro function spaces do not have the Radon–Nikodym property, are not locally uniformly convex and they are not dual spaces.