Convergence of p-Energy Forms on Homogeneous p.c.f Self-Similar Sets

In this paper, we give definitions of p-energy forms on homogenous p.c.f. self-similar sets and point that the domains of non-local p-energy form, local p-energy form are Lipschitz spaces B-p(,p)sigma, B-p,infinity(sigma), respectively. By constructing equivalent semi-norms of p-energy forms, we obtain the convergence of the B-p(,p)sigma-norms to the (sigma*)(B)(p,infinity)-norm as sigma up arrow sigma*, where the critical exponent sigma* is the supremum of sigma such that B-p,infinity(sigma) boolean AND C(K) is dense in C(K).