East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
권호 표지
DOI QR코드

DOI QR Code

DEGREE OF CONVERGENCE FOR FOURIER SERIES OF FUNCTIONS IN THE CLASS Lp-BV

  • Kim, Jaeman (Department of Mathematics Education Kangwon National University)
  • Received : 2018.11.22
  • Accepted : 2019.03.25
  • Published : 2019.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, the author introduces the class $L^p$-BV of functions which are of bounded variation in the sense of $L^p$-norm and investigates the degree of convergence for Fourier series of functions belonging to this class.

Keywords

References

  1. R. Bojanic, An estimate of the rate of convergence for Fourier series of functions of bounded variation, Publ.Inst.Math.(Beograd)(N.S.) (1979), 26, no. 40, 57-60.
  2. R.E. Castillo, and E. Trousselot, On functions of (p,${\alpha}$)-bounded variation, Real Anal.Exchange (2008/2009), 34, 49-60. https://doi.org/10.14321/realanalexch.34.1.0049
  3. G. Folland, Real analysis:Modern technique and their applications, 2nd ed, Wiley Interscience (1999).
  4. C. Jordan, Sur la series de Fourier, C.R.Math.Acad.Sci.Paris (1881), 2, 228-230.
  5. F. Moricz, and A.H. Siddiqi, A quantified version of the Dirichlet-Jordan test in $L^1$-norm, Rend.Circ.Mat.Palermo (2) (1996), 45, 19-24. https://doi.org/10.1007/BF02845086
  6. J. Musielak, and W. Orlicz, On generalized variations I, Studia Math. (1959), 18, 11-41. https://doi.org/10.4064/sm-18-1-11-41
  7. M. Shiba, On the absolute convergence of Fourier series of functions of class ${\Lambda}BV^{(p)}$, Sci.Rep.Fac.Ed.Fukushima Univ. (1980), 30, 7-10.
  8. E.C. Titchmarsh, The theory of functions, Oxford Univ. Press (1976).
  9. D. Waterman, On ${\Lambda}$-bounded variations, Studia Math. (1976), 57, 33-45. https://doi.org/10.4064/sm-57-1-33-45
  10. D. Waterman, Fourier series of functions of ${\Lambda}$-bounded variation, Pro.Amer.Math.Soc. (1979), 74, 119-123.
  11. A. Zygmund, Trigonometric Series, Vol. 1, Cambridge Univ. Press UK (1959).