Construction of self-similar energy forms and singularity of Sobolev spaces on Laakso-type fractal spaces

We construct self-similar $p$-energy forms $\mathscr{E}_p$ on a rich class of \emph{Laakso-type fractal spaces} and study the properties of the associated Sobolev spaces $\mathscr{F}_p$. The main result of the paper is the discovery of a new analytic phenomenon, which we refer to as \emph{singularit