Absolute convergence of multiple Fourier integrals

Yurii Kolomoitsev; Elijah Liflyand

doi:10.4064/sm214-1-2

Absolute convergence of multiple Fourier integrals

Yurii Kolomoitsev
, Elijah Liflyand

Department of Mathematics

NASU - Institute of Applied Mathematics and Mechanics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 Lp 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.

Original language	English
Pages (from-to)	17-35
Number of pages	19
Journal	Studia Mathematica
Volume	214
Issue number	1
DOIs	https://doi.org/10.4064/sm214-1-2
State	Published - 2013

Keywords

Fourier integral
Fourier multiplier
Hardy{Steklov inequality

Access to Document

10.4064/sm214-1-2

Cite this

@article{615dddd679f448aa81a20ae3420d903f,

title = "Absolute convergence of multiple Fourier integrals",

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 Lp 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.",

keywords = "Fourier integral, Fourier multiplier, Hardy\{Steklov inequality",

author = "Yurii Kolomoitsev and Elijah Liflyand",

year = "2013",

doi = "10.4064/sm214-1-2",

language = "אנגלית",

volume = "214",

pages = "17--35",

journal = "Studia Mathematica",

issn = "0039-3223",

publisher = "Institute of Mathematics, Polish Academy of Sciences",

number = "1",

}

TY - JOUR

T1 - Absolute convergence of multiple Fourier integrals

AU - Kolomoitsev, Yurii

AU - Liflyand, Elijah

PY - 2013

Y1 - 2013

N2 - 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 Lp 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.

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 Lp 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.

KW - Fourier integral

KW - Fourier multiplier

KW - Hardy{Steklov inequality

UR - https://www.scopus.com/pages/publications/84876039953

U2 - 10.4064/sm214-1-2

DO - 10.4064/sm214-1-2

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84876039953

SN - 0039-3223

VL - 214

SP - 17

EP - 35

JO - Studia Mathematica

JF - Studia Mathematica

IS - 1

ER -

Absolute convergence of multiple Fourier integrals

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this