Fourier Transforms in Generalized Lipschitz Classes

被引：3

作者：

Volosivets, S. S. ^{[1
]}

Golubov, B. I. ^{[2
]}

机构：

[1] Saratov NG Chernyshevskii State Univ, Dept Mech & Math, Saratov 410012, Russia

[2] State Univ, Moscow Inst Phys & Technol, Dolgoprudnyi 141700, Moscow Oblast, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2013年 / 280卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

Entire Function; STEKLOV Institute; Continuous Bounded Function; Fourier Integral; Ordinary Derivative;

D O I：

10.1134/S0081543813010070

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain sufficient conditions for the Fourier transform of a function f is an element of L-1(R) to belong to generalized Lipschitz classes defined by the modulus of smoothness of order m. The sharpness of these conditions is established in the cases when f(t) >= 0 on R or t f (t) >= 0 on R.

引用

页码：120 / 131

页数：12

共 9 条

[1] [Anonymous], 1977, Approximation of Multivariate Functions and Embedding Theorems
[2] Bari NK., 1956, Tr. Mosk. Mat. Obs, V5, P483
[3] Absolutely convergent Fourier integrals and classical function spaces
Moricz, Ferenc
[J]. ARCHIV DER MATHEMATIK, 2008, 91 (01) : 49 - 62
[4] Best possible sufficient conditions for the Fourier transform to satisfy the Lipschitz or Zygmund condition
Moricz, Ferenc
[J]. STUDIA MATHEMATICA, 2010, 199 (02) : 199 - 205
[5] FOURIER-TRANSFORMS AND THEIR LIPSCHITZ CLASSES
SAMPSON, G
TUY, H
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1978, 75 (02) : 519 - 537
[6] Tikhonov S, 2007, MATH INEQUAL APPL, V10, P229
[7] Timan A.F., 1960, Theory of Approximation of Functions of Real Variable
[8] Titchmarsh E. C., 1937, INTRO THEORY FOURIER
[9] Fourier transforms and generalized Lipschitz classes in uniform metric
Volosivets, S. S.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 383 (02) : 344 - 352

← 1 →