Absolute convergence of multiple Fourier integrals
Tom 214 / 2013
Studia Mathematica 214 (2013), 17-35 MSC: $\hskip -1pt$Primary 42B10; Secondary 42B15, 42A38, 42A45. DOI: 10.4064/sm214-1-2
Various new sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained. The results are given in terms of $L_p$ integrability of the function and its partial derivatives, each with a different $p$. These $p$ are subject to certain relations known earlier only for some particular cases. Sharpness and applications of the results obtained are also discussed.