$$p$$-Adic Hardy-Hilbert-Type Integral Operators on Block Spaces

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.