Equiconvergence of expansions in a multiple Fourier series and Fourier integral for summation over squares

In this work there are constructed a function $f(\overline x)\in L_1([-\pi,\pi]^2)$ such that the difference between the Fourier series expansion and the Fourier integral expansion for summation over squares diverges almost everywhere on $\{[-\pi,\pi]^2\}$, and a function $f(\overline x)\in L_p([-\pi,\pi]^N)$, $p>1$, $N\geqslant2$, for which the difference diverges at a point.
Bibliography: 5 titles.