On boundedness of four-dimensional Hausdorff matrices on the double Taylor sequence spaces

In this paper, we introduce the double Taylor sequence space Tpr,s consisting of all sequences whose doubly Taylor transforms of orders r,s are in the space Lp of non-absolute type which is a Banach space including the space Lp. Further, some inclusion relations concerning the space Tpr,s are given. Then, we focus on the evaluation of the exact values of the operator norm and lower bound of four-dimensional Hausdorff matrices as operators mapping the double sequence space Lp into the double Taylor sequence spaces Tpr,s. Some estimates are obtained. In particular, we apply our results to some special cases of four-dimensional Hausdorff matrices, such as Cesáro, Euler, Hölder and Gamma matrices.