Sufficient conditions for absolute convergence of multiple Fourier integrals

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.