A New Class of $$p$$-Adic Integral Operators and Applications

In this paper, we introduce and study a new class of $$p$$ -adic integral operators, induced by a homogeneous kernel, acting on the $$p$$ -adic weighted Lebesgue spaces. We obtain the sharp norm estimates for these operator. As applications, we establish some new $$p$$ -adic Hardy-Littlewood-Pólya-type inequalities with the best constants.