Pringsheim type tests on the pointwise convergence of integrals conjugate to double fourier integralsПриэнаки типа Прингсхейма для поточечной сходимости двойных тригонометрически сопряженных интегралов Фурье

We prove sufficient conditions for the convergence of the integrals conjugate to the double Fourier integral of a complex-valued function f ∈ L1 (ℝ2) with bounded support at a given point (x0, g0) ∈ ℝ2. It turns out that this convergence essentially depends on the convergence of the integral conjugate to the single Fourier integral of the marginal functions f(x, y0), x ∈ ℝ, and f(x0, y), y ∈ ℝ, at x:= x0 and y:= y0, respectively. Our theorems apply to functions in the multiplicative Lipschitz and Zygmund classes introduced in this paper.