A Dini type test on the pointwise convergence of double Fourier integrals |
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Authors: | Ferenc Móricz |
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Affiliation: | 1. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720, Szeged, Hungary
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Abstract: | We give sufficient conditions for the convergence of the double Fourier integral of a complex-valued function f ∈ L 1(?2) with bounded support at a given point (x 0,y 0) ∈ ?2. It turns out that this convergence essentially depends on the convergence of the single Fourier integrals of the marginal functions f(x,y 0), x ∈ ?, and f(x 0,y), y ∈ ?, at the points x:= x 0 and y:= y 0, respectively. Our theorem applies to functions in the multiplicative Zygmund classes of functions in two variables. |
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