Sufficient conditions for absolute convergence of multiple Fourier integrals

2011/08/27 by Kolomoitsev, Yu., Liflyand, E.
#42A38 #42A45 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary 42B10 #Secondary 42B15

paper · doi:10.48550/arxiv.1108.5470

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 L^p 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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