Local fractal functions and function spaces

Original · EN

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 Cˢ, and the Sobolev spaces Wᵐ,ᵖ.