Illinois Journal of Mathematics

Alternate characterizations of bounded variation and of general monotonicity for functions

Barry Booton

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Abstract

We find necessary and sufficient conditions for a function to be equal almost everywhere to a function of bounded variation. These results can be applied to broaden the class of general monotone functions.

Article information

Source
Illinois J. Math., Volume 60, Number 2 (2016), 551-561.

Dates
Received: 8 July 2016
Revised: 25 January 2017
First available in Project Euclid: 11 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1499760022

Digital Object Identifier
doi:10.1215/ijm/1499760022

Mathematical Reviews number (MathSciNet)
MR3680548

Zentralblatt MATH identifier
1371.26014

Subjects
Primary: 26A45: Functions of bounded variation, generalizations 26A48: Monotonic functions, generalizations

Citation

Booton, Barry. Alternate characterizations of bounded variation and of general monotonicity for functions. Illinois J. Math. 60 (2016), no. 2, 551--561. doi:10.1215/ijm/1499760022. https://projecteuclid.org/euclid.ijm/1499760022


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References

  • J. Appell, J. Banaś and N. Merentes, Bounded variation and around, DeGruyter Studies in Nonlinear Analysis and Applications, de Gruyter, Berlin, 2014.
  • A. S. Belov, Remarks on mean convergence (boundedness) of partial sums of trigonometric series, Mat. Zametki 71 (2002), no. 6, 807–817. English translation in: Math. Notes 71 (2002), nos. 5–6, 739–748.
  • Y. Brudnyi, Multivariate functions of bounded $(k,p)$-variation, Banach spaces and their applications in analysis (Oxford, OH, 2006), de Gruyter, Berlin, 2007, pp. 37–57.
  • E. Liflyand and S. Tikhonov, The Fourier transforms of general monotone functions, Analysis and mathematical physics, Trends in Mathematics, Birkhäuser, Basel, 2009, pp. 377–395.
  • E. Liflyand and S. Tikhonov, A concept of general monotonicity and applications, Math. Nachr. 284 (2011), no. 8–9, 1083–1098.
  • S. Tikhonov, Trigonometric series with general monotone coefficients, J. Math. Anal. Appl. 326 (2007), no. 1, 721–735.