Let = be a non-negative matrix. Denote by the supremum of those , satisfying the following inequality:
where , , and also is increasing, non-negative sequence of real numbers. If we used instead of The purpose of this paper is to establish a Hardy type formula for , where is Hausdorff matrix and A similar result is also established for where In particular, we apply our results to the Cesaro matrices, Holder matrices and Gamma matrices. Our results also generalize some works due to R. Lashkaripour and D. Foroutannia . Moreover, in this study we extend some results mentioned in  and .