. From these observations, weighted-norm estimates for first and higher derivatives by x will be obtained, using a generalized Hardy inequality. The results in turn imply the generalized Hardy inequality upon which
they depend and will hold true in any weighted norm for which the generalized Hardy is true.
and Orlicz spaces XΦ obtained by replacing the space L1 in the classical construction by an arbitrary Banach function space X. Our main aim is to focus on the task to study inequalities in such spaces. We prove a number of new inequalities and also
natural generalizations of some classical ones (e.g., Minkowski’s, H�lder’s and Young’s inequalities). Moreover, a number
of other basic facts for further study of inequalities and function spaces are included.