Estimates for $$p$$ -adic fractional integral operators and their commutators on $$p$$ -adic mixed central Morrey spaces and generalized mixed Morrey spaces

In this paper, we define the \(p\)-adic mixed Morrey type spaces and study the boundedness of \(p\)-adic fractional integral operators and their commutators on these spaces. More precisely, we first obtain the boundedness of \(p\)-adic fractional integral operators and their commutators on \(p\)-adic mixed central Morrey spaces. Moreover, we further extend these results on \(p\)-adic generalized mixed Morrey spaces, when a symbol function \(b\) belongs to the \(p\)-adic generalized mixed Campanato spaces.