Discrete Morrey spaces over Z and local estimation of the discrete Hilbert transform

The aim of this article is to investigate structural properties of discrete Morrey spaces ℓ p,λ (Z) and their weak counterparts wℓ p,λ (Z).We establish continuous embedding theorems both within the class of discrete Morrey spaces and within weak discrete Morrey spaces, providing explicit conditions on the parameters p and λ.Furthermore, based on a local estimate for the discrete Hilbert transform derived in this work, we prove its strong and weak boundedness on discrete Morrey spaces over Z.