Operator norms of four-dimensional Hausdorff matrices on the double Euler sequence spaces

Abstract

In this paper, the double Euler sequence space is introduced which consists of all sequences whose double Euler transforms of orders are in the space . It is shown that the space is a normed space which includes the space and is linearly isomorphic to for Furthermore, some inclusion relations concerning the space are given as well as the basis for is constructed where Moreover, a Hardy type formula is obtained for the operator norms of the class of four-dimensional Hausdorff matrices as operators selfmap of the space . A similar result is also established in the case that this matrices map into . In particular, we apply our results to some special four-dimensional Hausdorff matrices such as four-dimensional Cesàro, Euler, Hölder and Gamma matrices.