Complex powers of the Laplacian on affine nested fractals as Calderón-Zygmund operators

(Communicated by the associate editor name) Abstract. We give the first natural examples of Calderón-Zygmund operators in the theory of analysis on post-critically finite self-similar fractals. This is achieved by showing that the purely imaginary Riesz and Bessel potentials on nested fractals with 3 or more boundary points are of this type. It follows that these operators are bounded on Lp, 1 < p < ∞ and satisfy weak 1-1 bounds. The analysis may be extended to infinite blow-ups of these fractals, and to product spaces based on the fractal or its blow-up. 1. Introduction. Comple