Absolute convergence of Fourier–Haar series of functions of two variables

It is well-known that if a one-dimensional function is continuously differentiable on $[0,1]$, then its Fourier–Haar series converges absolutely. On the other hand, if a function of two variables has continuous partial derivatives $f_x'$ and $f_y'$ on $T^2$, then its Fourier series does not necessarily absolutely converge with respect to a multiple Haar system (see [1]). In this paper we state sufficient conditions for the absolute convergence of the Fourier–Haar series for two-dimensional continuously differentiable functions