LOCAL FRACTAL FUNCTIONS AND FUNCTION SPACES

Abstract. We introduce local iterated function systems and present some of their basic properties. A new class of local attractors of local iterated function systems, namely local fractal functions, is constructed. We derive formulas so that these local fractal functions become elements of various function spaces, such as the Lebesgue spaces Lp, the smoothness spaces Cn, the homogeneous Hölder spaces Ċs, and the Sobolev spaces Wm,p