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  • 1 University of Szeged Bolyai Institute Aradi vértanúk tere 1 6720 Szeged Hungary
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Abstract  

We prove sufficient conditions for the convergence of the integrals conjugate to the double Fourier integral of a complex-valued function fL1 (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.