Sufficient conditions for absolute convergence of multiple Fourier integrals

TL;DR

This paper establishes new sufficient conditions based on $L^p$ integrability for representing multivariable functions as absolutely convergent Fourier integrals, extending known relations and discussing sharpness and applications.

Contribution

It introduces generalized $L^p$-based conditions for absolute convergence of multiple Fourier integrals, broadening previous specific case results.

Findings

New $L^p$ conditions for absolute convergence

Relations between integrability of functions and derivatives

Applications demonstrating the sharpness of results

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.