Browse > Article
http://dx.doi.org/10.7858/eamj.2019.026

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

Kim, Jaeman (Department of Mathematics Education Kangwon National University)
Publication Information
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
the class $L^p$-BV; the degree of convergence for Fourier series;
Citations & Related Records
연도 인용수 순위
  • Reference
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.   DOI
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.   DOI
6 J. Musielak, and W. Orlicz, On generalized variations I, Studia Math. (1959), 18, 11-41.   DOI
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.   DOI
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).