Hölder extension of a function defined on a Sierpinski gasket

We construct a linear extension operator Π that extends a function u defined on a Sierpinski gasket S which satisfies the Hölder estimate |u(x)− u(y)| ≤ C0|x− y| for all x, y on S, to a larger domain Ω ⊆ R. The extension function Πu is defined everywhere in Ω, is Hölder continuous everywhere in Ω, corresponds with u at every point on S and satisfies the estimate |Πu|Ω,β ≤ C‖u‖S,β with a constant C independent of u. Our approach is more constructive then the standard approach and utilizes both the iterative nature and the self similarity of the Sierpinski gasket to construct an extension function.