The difference sequence spaces @?"~(@D),c(@D) and c"0(@D) were studied by Kizmaz [Canad. Math. Bull. 24 (2) (1981) 169]. The sequence spaces a"0^r and a"c^r have been recently defined and examined by Aydin and Basar in [Hokkaido Math. J., in press]. The main purpose of the present paper is to introduce the spaces a^r"0(@D) and a^r"c(@D) of difference sequences. Moreover, it is proved that the spaces a^r"0(@D) and a^r"c(@D) are the BK-spaces including the spaces c"0 and c, and some inclusion relations have been given. It is also proved that the sequence space a"0^r has AD property while the space a"0^r(@D) has not. Furthermore, the basis and the @a-, @b- and @c-duals of the spaces a^r"0(@D) and a^r"c(@D) have been determined. The last section of the paper has been devoted to theorems on the characterizations of the matrix classes (a^r"c(@D):@?"p) and (a^r"c(@D):c), and the characterizations of some other matrix classes have been obtained by means of a given basic lemma, where 1=
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