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.