LAUSR

In Hardy (Proc Camb Philos 19:86–95, 1916), Hardy defined the normed spaces $$\mathcal {C}_{r}$$Cr and $$\mathcal {C}_{r0}$$Cr0 of all regularly convergent and regularly null double sequences and made convergence factor calculations (i.e. some beta-dual calculations). In this paper, we extend these spaces to the paranormed spaces $$\mathcal {C}_{r}(t)$$Cr(t) and $$\mathcal {C}_{r0}(t)$$Cr0(t). Also, we define the paranormed spaces $$\mathcal {C}_{tr}(t)$$Ctr(t) and $$\mathcal {C}_{tr0}(t)$$Ctr0(t) of all totally regularly convergent and totally regularly null double sequences. We examine some topological properties of these spaces and determine their alpha-, beta- and gamma-duals.