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Nonlinear Energy Forms and Lipschitz Spaces on the Koch Curve

2002; Volume: 9; Issue: 1 Linguagem: Inglês

2363-6394

Raffaela Capitanelli, Maria Rosaria Lancia,

Mathematical Analysis and Transform Methods

In the quadratic case p = 2, constructions of this type are standard and have been done for various fractals K like the Sierpinski gasket, the Koch curve and more general simple nested fractals: in these cases, the energy functionals E (2) are Dirichlet forms, whose domains DE(2) are the fractal analogue of the Sobolev space W . Always in the case p = 2, these spaces W (K) ≡ DE(2)(K) have been put in relation with the theory of Lipschitz spaces Lipα,Df (2,∞, K); in particular, in Jonsson [5] first and later also in Lancia and Vivaldi [9], Paluba [13] and Kumagai [8], for various examples of fractals K the following characterization has been given