  It is proved that, under certain restrictions on weights, a pair of weighted
Hardy spaces on the two-dimensional torus is K-closed in the pair of the
corresponding weighted Lebesgue spaces. By now, K-closedness of Hardy spaces on
the two-dimensional torus was considered either in the case of no weights or in
the case of weights that split into a product of two functions of one variable
(the so-called "split weights"). Here the case of certain nonsplit weights is
studied.
