In this paper, we established some sufficient conditions for the boundedness of the Hardy–Littlewood maximal operators and the Hausdorff operators on $p$-adic Herz spaces and $p$-adic local block spaces with variable exponents. In particular, the boundedness of the $p$-adic maximal commutator operators, the $p$-adic Hardy–Littlewood average operators, and the $p$-adic Hardy-Hilbert operators on such spaces was also discussed.

The aim of this paper is to establish some sufficient conditions for the boundedness of commutators of Hardy-Cesàro operators with symbols in central BMO spaces with variable exponent on some function spaces such as the local central Morrey, Herz, and Morrey-Herz spaces with variable exponents.