Multidimensional Linear Functional Connected with Double Strong Cesàro Summability

Abstract

In 1964 Borwein presented functional characterization of the normed linear spaces wp and Wp. These two spaces are clearly linked to Cesaro summability [C, 1] in particular it should be noted that a sequence x in wp if and only if x is Cesaro summable. The goal of this paper includes extension of these notions to double function space thus producing multidimensional analog of Borwein’s results.