Abstract
For a class of closed sets F ⊂ Rn admitting a regular sequence of triangulations or generalized triangulations, the analogues on F of the Faber—Schauder and Franklin bases are discussed. The characterizations of the Besov spaces on F in the terms of coefficients of functions with respect to these bases are proved. As a consequence, analogous characterizations of the Besov spaces on some fractal domains (including the Sierpinski gasket and the von Koch curve) by coefficients of functions with respect to the wavelet bases constructed in [26] are obtained.
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