Sharp weak bounds for discrete Hardy operator on discrete central Morrey spaces

Abstract

In this note, we introduce the discrete (weak) central Morrey spaces, which are central versions of discrete (weak) Morrey spaces. The sharp bounds for discrete Hardy operator from discrete central Morrey spaces to discrete weak central Morrey spaces are proven to be equal to 1. As an application, we obtain the weak version of the well-known discrete Hardy inequality.

Keywords

• discrete hardy operator
• sharp bound
• discrete central morrey space
• discrete lebesgue space