TRANSITION DENSITY ESTIMATES FOR BROWNIAN-MOTION ON AFFINE NESTED FRACTALS

A class of affine nested fractals is introduced which have different s cale factors for different similitudes but still have the symmetry ass umptions of nested fractals. For these fractals estimates on the trans ition density for the Brownian motion are obtained using the associate d Dirichlet form. An upper bound for the diagonal can be found using a Nash-type inequality, then probabilistic techniques are used to obtai n the off-diagonal bound. The approach differs from previous treatment s as it uses only the Dirichlet form and no estimates on the resolvent . The bounds obtained are expressed in terms of an intrinsic metric on the fractal.