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.