On the growth order of sequences of double rectangular Fourier sums for functions from the classes $\varphi(L)$

We obtain estimates for the growth order of arbitrary sequences of rectangular partial sums of double trigonometric Fourier series for functions from the classes $\varphi(L)$, which are intermediate between $L\log^+L_{[0,2\pi)^2}$; and $L(\log^+L)^2_{[0,2\pi)^2}$.