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The essential aim of this paper is to define weighted q-Hardy-littlewood-type maximal operator by means of p-adic q-invariant distribution on Zp. Moreover, we give some interesting properties concerning this type maximal operator.

A NOTE ON THE WEIGHTED q-HARDY-LITTLEWOOD-TYPE MAXIMAL OPERATOR WITH RESPECT TO q-VOLKENBORN INTEGRAL IN THE p-ADIC INTEGER RING