2 papers
math.MG2025
Construction of self-similar energy forms and singularity of Sobolev spaces on Laakso-type fractal spaces
Riku Anttila, Sylvester Eriksson-Bique, Ryosuke Shimizu
We construct self-similar -energy forms on a rich class of \emph{Laakso-type fractal spaces} and study the properties of the associated Sobolev spaces $\mathscr{…
math.FA2024
Finite dimensionality of Besov spaces and potential-theoretic decomposition of metric spaces
Takashi Kumagai, Nageswari Shanmugalingam, Ryosuke Shimizu
In the context of a metric measure space , we explore the potential-theoretic implications of having a finite-dimensional Besov space. We prove that if the dimension of th…