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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm214-1-2,
author = {Yurii Kolomoitsev and Elijah Liflyand},
title = {Absolute convergence of multiple Fourier integrals},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {17-35},
zbl = {1272.42007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm214-1-2}
}
Yurii Kolomoitsev; Elijah Liflyand. Absolute convergence of multiple Fourier integrals. Studia Mathematica, Tome 215 (2013) pp. 17-35. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm214-1-2/