On the Taylor sequence spaces and upper boundedness of Hausdorff matrices and Nörlund matrices

In this paper, the Taylor sequence space tpθ of non-absolute type is introduced which consists of all sequences whose Taylor transforms of order θ,(0<θ<1), are in the space ℓp. It is shown that the space tpθ is a normed space which includes the space ℓp where 1≤p≤∞. Moreover, in this paper a general upper estimate is obtained for the norm of Hausdorff matrices and Nörlund matrices as operators from ℓp into the Taylor sequence space tpθ. Finally, the results are extended to the matrix domain of an arbitrary invertible matrix E in the sequence space ℓp.