2 papers
math.FA2025
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 t…
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 as normalized limits of discretized -energies on a rich class of Laakso-type fractal spaces. Collectively, we refer to them as IGS-fra…