Let 0 < s < ?. In this study, we introduce the double sequence space Rqt(Ls)
as the domain of four dimensional Riesz mean Rqt in the space Ls of
absolutely s-summable double sequences. Furthermore, we show that Rqt(Ls) is
a Banach space and a barrelled space for 1 ? s < 1 and is not a barrelled
space for 0 < s < 1. We determine the ?- and ?(?)-duals of the space Ls for
0 < s ? 1 and ?(bp)-dual of the space Rqt(Ls) for 1 < s < 1, where ? ? {p,
bp, r}. Finally, we characterize the classes (Ls:Mu), (Ls:Cbp), (Rqt(Ls)
: Mu) and (Rqt(Ls):Cbp) of four dimensional matrices in the cases both 0 <
s < 1 and 1 ? s < 1 together with corollaries some of them give the
necessary and sufficient conditions on a four dimensional matrix in order to
transform a Riesz double sequence space into another Riesz double sequence
space.
