FRACTAL GEOMETRY OF WEIERSTRASS-TYPE FUNCTIONS

The aim of this paper is twofold. First, with reference to Refs. 1 and 2 we show maximal and minimal box and Hausdorff dimensions over all continuous real functions compactly supported on ℝn, with integrability 0 0. We estimate also the box dimensions of trigonometrical Weierstrass-type functions. Secondly, we investigate some criteria in order to decide when the graph of a function is not a d-set. Moreover, for each d between n and n + 1 we construct a function on [0,1]n the graph of which is a d-set.