On an integral inequality

In this paper we deduce an integral inequality which is an analog of a known two-parameter inequality of Hardy and Littlewood (1], Theorem 382). A need for inequalities of a similar type arises, for example, in studying the imbedding of the functional spaces B _p ^l in the space L_q if this study leads to a basis of the method of integral representations of functions.Translated from Matematicheskie Zametki, Vol. 6, No. 2, pp. 139–148, August, 1969.