Real Analysis Exchange

On Absolute Convergence of Fourier Integrals

E. Liflyand

Full-text: Open access

Abstract

New sufficient conditions for representation of a function as an absolutely convergent Fourier integral are obtained in the paper.

Article information

Source
Real Anal. Exchange, Volume 36, Number 2 (2010), 353-360.

Dates
First available in Project Euclid: 11 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.rae/1321020505

Mathematical Reviews number (MathSciNet)
MR3016721

Zentralblatt MATH identifier
1250.42025

Subjects
Primary: 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Secondary: 42A25

Keywords
Fourier integral absolute convergence Hardy inequality

Citation

Liflyand, E. On Absolute Convergence of Fourier Integrals. Real Anal. Exchange 36 (2010), no. 2, 353--360. https://projecteuclid.org/euclid.rae/1321020505


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References

  • O. V. Besov, Hörmander's theorem on Fourier multipliers, Trudy Mat. Inst. Steklov 173 (1986), 164–180 (Russian). - English transl.: Proc. Steklov Inst. Math. 4 (1987), 4–14.
  • I. I. Hirschman, Jr., On multiplier transformations, I, Duke Math. J. 26 (1959), 221–242; II, ibid 28 (1961), 45–56.
  • J.-P. Kahane, Séries de Fourier absolument convergentes, Springer, Berlin, 1970.
  • A. Kufner, L. E. Persson, Weighted Inequalities of Hardy Type, World Scientific, 2003.
  • E. Liflyand and R. Trigub, Conditions for the absolute convergence of Fourier integrals, J. Approx. Theory, 163 (2011), 438–459.
  • E. Liflyand and R. Trigub, On the Representation of a Function as an Absolutely Convergent Fourier Integral, Trudy Mat. Inst. Steklov, 269 (2010), 153–166 (Russian). - English transl.: Proc. Steklov Inst. Math., 269 (2010), 146–159.
  • S. G. Samko and G. S. Kostetskaya, Absolute integrability of Fourier integrals, Vestnik RUDN (Russian Peoples Friendship Univ.), Math., 1 (1994), 138–168.
  • E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970.
  • R. M. Trigub, Absolute convergence of Fourier integrals, summability of Fourier series, and polynomial approximation of functions on the torus, Izv. Akad. Nauk SSSR, Ser.Mat., 44 (1980), 1378–1408 (Russian). - English transl.: Math. USSR Izv., 17 (1981), 567–593.
  • R. M. Trigub and E. S. Belinsky, Fourier Analysis and Appoximation of Functions, Kluwer, 2004.