Upper bounds of some matrix operators on binomial and Orlicz-binomial double sequence spaces

Abstract

In this article, we introduce binomial double sequence space bk(α,β;γ,δ)(1≤k≤∞) and Orlicz-binomial double sequence space bφ(α,β;γ,δ), and obtain certain inclusion results related to these spaces. We further focus on estimating the upper bounds for ∥M∥Lk,bk(α,β;γ,δ) and ∥M∥Lφ,bφ(α,β;γ,δ), where M is four dimensional Hausdorff matrix or four dimensional Nörlund matrix. We establish a Hardy type inequality in the case of four dimensional Hausdorff matrix.