Pringsheim type tests on the pointwise convergence of integrals conjugate to 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 prove sufficient conditions for the convergence of the integrals conjugate to the double Fourier integral of a complex-valued function f ∈ L 1 (?2) with bounded support at a given point (x 0, g 0) ∈ ?2. 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, y 0), x ∈ ?, and f(x 0, y), y ∈ ?, at x:= x 0 and y:= y 0, respectively. Our theorems apply to functions in the multiplicative Lipschitz and Zygmund classes introduced in this paper. |
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