Abstract. The well-known inequalities of G. H. Hardy and J. E. Littlewood [1] play very important role in the proof of many theorems concerning convergence or summability of orthogonal series. Recently, L. Leindler proved a number of new inequalities of Hardy--Littlewood type (see, for example, [3], [4], [5], and references cited there). The aim of the present paper is to prove a Hardy--Littlewood type inequality for double numerical series.

AMS Subject Classification (1991): 40A05

Received January 29, 1996. (Registered under 5715/2009.)