Absolute convergence of multiple Fourier integrals

Yurii Kolomoitsev, and Elijah Liflyand. "Absolute convergence of multiple Fourier integrals." Studia Mathematica 214.1 (2013): 17-35. <http://eudml.org/doc/285922>.

@article{YuriiKolomoitsev2013,
abstract = {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.},
author = {Yurii Kolomoitsev, Elijah Liflyand},
journal = {Studia Mathematica},
keywords = {Fourier integral; Fourier multiplier; Hardy-Steklov inequality},
language = {eng},
number = {1},
pages = {17-35},
title = {Absolute convergence of multiple Fourier integrals},
url = {http://eudml.org/doc/285922},
volume = {214},
year = {2013},
}

TY - JOUR
AU - Yurii Kolomoitsev
AU - Elijah Liflyand
TI - Absolute convergence of multiple Fourier integrals
JO - Studia Mathematica
PY - 2013
VL - 214
IS - 1
SP - 17
EP - 35
AB - 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.
LA - eng
KW - Fourier integral; Fourier multiplier; Hardy-Steklov inequality
UR - http://eudml.org/doc/285922
ER -