Analysis on metric spaces emerged in the 1990s as an independent research field providing
a unified treatment of first-order analysis in diverse and potentially nonsmooth settings …

This book gives a comprehensive and self-contained introduction to the theory of symmetric
Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible …

TWO-SIDED ESTIMATES OF HEAT KERNELS ON METRIC MEASURE SPACES Page 1 The
Annals of Probability 2012, Vol. 40, No. 3, 1212-1284 DOI: 10.1214/11-AOP645 © Institute of …

We give an overview over the application of functional equations, namely the classical
Poincaré and renewal equations, to the study of the spectrum of Laplace operators on self …

We construct and investigate $(1, p) $-Sobolev space, $ p $-energy, and the corresponding
$ p $-energy measures on the planar Sierpi\'{n} ski carpet for all $ p\in (1,\infty) $. Our …

In the ordinary theory of Sobolev spaces on domains of Rn, the p-energy is defined as the
integral of jrf jp. In this paper, we try to construct a p-energy on compact metric spaces as a …

With a view toward fractal spaces, by using a Korevaar–Schoen space approach, we
introduce the class of bounded variation (BV) functions in the general framework of strongly …

We construct symmetric self-similar Dirichlet forms on unconstrained Sierpinski carpets,
which are natural extension of planar Sierpinski carpets by allowing the small cells to live off …

On fractals, spectral functions such as heat kernels and zeta functions exhibit novel features,
very different from their behaviour on regular smooth manifolds, and these can have …

We introduce the notion of conformal walk dimension, which serves as a bridge between
elliptic and parabolic Harnack inequalities. The importance of this notion is due to the fact …