7 citations · 38 across the 29 of their papers we have counts for
4 papers · 2 filters
Brownian motion on the golden ratio Sierpinski gasket
Shiping Cao, Hua Qiu
We construct a strongly local regular Dirichlet form on the golden ratio Sierpinski gasket, which is a self-similar set without any finitely ramified cell structure, via a study on…
Existence and uniqueness of diffusions on the Julia sets of Misiurewicz-Sierpinski maps
Shiping Cao, Malte S. Hassler, Hua Qiu +2
We study the balanced resistance forms on the Julia sets of Misiurewicz-Sierpinski maps, which are self-similar resistance forms with equal weights. In particular, we use a theorem…
Equivalence of Besov spaces on p.c.f. self-similar sets
Shiping Cao, Hua Qiu
On p.c.f. self-similar sets, of which the walk dimensions of heat kernels are in general larger than 2, we find a sharp region where two classes of Besov spaces, the heat Besov spa…
Sobolev spaces on p.c.f. self-similar sets: boundary behavior and interpolation theorems
Shiping Cao, Hua Qiu
We study the Sobolev spaces and on p.c.f. self-similar sets in terms of the boundary behavior of functions. First, for , we make an exact des…