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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.
Acknowledgements
The author has benefited a lot from the referee’s report. So, I thank the reviewer for his/her careful reading and making some useful comments which improved the presentation of the paper.
Notes
No potential conflict of interest was reported by the author.
Dedicated to Imam Hassan Mojtaba (as).