Real Analysis Exchange

A Note on the Harmonic Derivative

Tord Sjödin

Full-text: Open access


We characterize ordinary differentiability in terms on the harmonic derivative and a local Lipschitz type condition and apply the result to $C^{k,1}$-functions.

Article information

Real Anal. Exchange, Volume 30, Number 1 (2004), 11-22.

First available in Project Euclid: 27 July 2005

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26B05: Continuity and differentiation questions 26B35: Special properties of functions of several variables, Hölder conditions, etc. 31B05: Harmonic, subharmonic, superharmonic functions

Taylor polynomial harmonic derivative approximative derivative Lipschitz condition


Sjödin, Tord. A Note on the Harmonic Derivative. Real Anal. Exchange 30 (2004), no. 1, 11--22.

Export citation


  • A. M. Bruckner, Differentiation of real functions, Lecture Notes in Mathematics, 659, Springer Verlag, Heidelberg, 1978.
  • H. Federer, Geometric measure theory, Grundlehren der matematischen Wissenschaften, Band 153, Springer Verlag, Berlin-Heidelberg-New York, 1969.
  • T. Sjödin, On $L^p$-differentiability of Bessel potentials and difference properties of functions, Studia Math., 74 (1982), 153–168.
  • T. Sjödin, On Ordinary Differentiability of Bessel Potentials, Ann. Polonici Math., 44 (1984), 326–352.
  • E. M. Stein, Singular integrals and differentiability properties of functions, Princeton University Press, Princeton, New Jersey, 1970.
  • B-M. Stocke, Differentiability of Bessel potentials and Besov functions, Ark. Mat., 22 (1984) 2, 269–286.
  • B. M. Zibman, Some characterizations of the $n$-dimensional Peano derivative, Studia Math., 63 (1978) 1, 89–110.