Characterizations of some operators on the vanishing generalized Morrey spaces with variable exponent

In this paper we will give some characterizations for the boundedness of the maximal operators, potential operators and singular integral operators on the vanishing generalized Morrey spaces VLΠp(⋅),φ(Ω) with variable exponent p(⋅)p(⋅) and bounded set Ω. Moreover, we also obtain some corresponding results for unbounded set Ω on such these spaces.