  In terms of the Fourier-Haar coefficients, a criterion is obtained for the
function $f (x_1,x_2)$ to belong to the net space $N_{\bar{p},\bar{q}}(M)$ and
to the Lebesgue space $L_{\bar{p}}[0,1]^2$ with mixed metric, where
$1<\bar{p}<\infty$, $0<\bar{q}\leq\infty$, $\bar{p}=(p_1,p_2)$,
$\bar{q}=(q_1,q_2)$, $M$ is the set of all rectangles in $\mathbb{R}^2$. We
proved the Hardy-Littlewood theorem for multiple Fourier-Haar series.
