On two weight criterions for the hardy littlewood maximal operator in bfs

Our aim of this paper is to prove two-weight criterions for the Hardy-Littlewood maximal operator from weighted Lebesgue spaces into Banach function spaces (BFS). We used boundedness of geometric mean operator and sufficient condition on the weights for boundedness of certain sublinear operator from weighted Lebesgue spaces into weighted Musielak-Orlicz spaces