Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 37, 2012, 509-523

HARMONIC FUNCTIONS REPRESENTATION OF BESOV-LIPSCHITZ FUNCTIONS ON NESTED FRACTALS

Mats Bodin and Katarzyna Pietruska-Paluba

Umeå University, Department of Ecology and Environmental Science
SE-901 87 Umeå, Sweden; mats.bodin 'at' emg.umu.se

University of Warsaw, Institute of Mathematics
ul. Banacha 2, 02-097 Warsaw, Poland; kpp 'at' mimuw.edu.pl

Abstract. R.S. Strichartz proposes a discrete definition of Besov spaces on self-similar fractals having a regular harmonic structure. In this paper, we characterize some of these Hölder-Zygmund and Besov-Lipschitz functions on nested fractals by means of the magnitude of the coefficients of the expansion of a function in a continuous piecewise harmonic base.

Key words: Besov spaces, Besov functions, Hölder functions, nested fractals, harmonic functions.

Reference to this article: M. Bodin and K. Pietruska-Paluba: Harmonic functions representation of Besov-Lipschitz functions on nested fractals. Ann. Acad. Sci. Fenn. Math. 37 (2012), 509-523.

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doi:10.5186/aasfm.2012.3735