Domain of difference matrix of order one in some spaces of double sequences
In this study, we define the spaces $\mathcal{M}_{u}(Δ),\mathcal{C}_{p}(Δ),\mathcal{C}_{0p}(Δ), \mathcal{C}_{r}(Δ)$ and $\mathcal{L}_{q}(Δ)$ of double sequences whose difference transforms are bounded , convergent in the Pringsheim's sense, null in the Pringsheim's sense, both convergent in the Pringsheim's sense and bounded, regularly convergent and absolutely $q-$summable, respectively, and also examine some inclusion relations related to those sequence spaces. Furthermore, we show that these sequence spaces are Banach spaces . We determine the alpha-dual of the space $\mathcal{M}_{u}(Δ)$ and the $β(v)-$dual of the space $\mathcal{C}_η(Δ)$ of double sequences, where $v,η\in \{p,bp,r\}$. Finally, we characterize the classes $(μ:\mathcal{C}_{v}(Δ))$ for $v\in \{p,bp,r\}$ of four dimensional matrix transformations, where $μ$ is any given space of double sequences.