Abstract
In this paper, we introduce the concepts of central \((r, \alpha)\) -block and block spaces \(\mathfrak{B}_{r,\alpha}(\mathbb{Q}_p)\) over the \(p\) -adic field. The duality and Fatou property of such spaces are examined. We also study mapping properties of \(p\) -adic Hardy-Hilbert-type integral operators in the framework of such block spaces. As an application, we also establish \(p\) -adic Hardy, Hilbert, and Hardy-Littlewood-Pólya inequalities for block spaces.
