Complementary Results on the Boundedness Problem of Factorizable Four-Dimensional Matrices

Abstract

In this paper, the boundedness problem of factorizable four-dimensional matrices on the space of double sequences is investigated. As an application of our results, the lower bounds and the operator norms of four-dimensional Cesaro matrix and four-dimensional Copson matrix are obtained, which provide an extension of Hardy’s discrete inequality and Copson’s discrete inequality to double series, respectively. Finally, we present complementary results for the operator norm and lower bound of the four-dimensional Hausdorff matrices.