AKIN, Lutfi2019-05-242019-05-242019-03-15978-605-7631-45-9https://hdl.handle.net/20.500.12514/689Operator theory studied by very mathematicians, we refer to [1,2,3,4,5]. Compactification of weighted Hardy operator in variable exponent Lebesgue spaces has been proof by [6]. Generalized duality of some Banach function spaces has been proof by [7]. On two weight criterions for the Hardy-Littlewood maximal operator in BFS has been proven, we refer to [8]. A Characterization of Approximation of Hardy Operators in VLS has been proven by [9]. We know that it is established an integraltype necessary and sufficient condition on weights which provides the boundedness of the Hardy-Littlewood maximal operator from weighted Lebesgue spaces into p-convex weighted BFS, we refer to [11].eninfo:eu-repo/semantics/openAccessBook Chapter