Sufficient conditions for absolute convergence of multiple Fourier integrals
Abstract
Various new sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained in the paper. The results are given in terms of Lp integrability of the function and its partial derivatives, each with the corresponding p. These p are subject to certain relations known earlier only for some particular cases. Sharpness and applications of the obtained results are also discussed.
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