Estimation of upper bounds of certain matrix operators on Binomial weighted sequence spaces

Abstract

In this article, we introduce binomial weighted sequence spaces $$b_p^{r,s}(w)$$ $$(1\le p<\infty )$$ , where $$w=(w_n)$$ is a non-negative decreasing sequence of real numbers, and investigate some topological and inclusion properties of the new spaces. We give an upper estimation of $$\left\| A\right\| _{\ell _p(w),b_p^{r,s}(w)}$$ , where A is the Hausdorff matrix operator or Norlund matrix operator. A Hardy type formula is established in the case of Hausdorff matrix operator. In the final section, we give an upper estimation for the transpose of Norlund matrix as an operator from $$\ell _p$$ to $$b_p^{r,s}$$ .