REAL-VALUED FUNCTIONS OF FINITE ENERGY ON THE SIERPINSKI GASKET
Brigitte E. Breckner · 2013
We present, including all necessary computation, the harmonic ex- tension procedure on the Sierpinski gasket in the n-dimensional Euclidean space. Thus we complete the results of (10) where this procedure is performed only in the cases n2f1; 2g. Moreover, we derive from this procedure certain properties of real-valued functions of nite energy dened on the Sierpinski gasket. We stress on the Holder continuity, since we haven't found in the literature a proof for it in the case n 3. MSC 2010. 28A80, 49J52.