12 papers
Local and non-local -energies on metric measure spaces
Meng Yang
For , we study subordination phenomena for local and non-local regular -energies on metric measure spaces. Under suitable geometric assumptions, we show that if a local reg…
Energy inequalities for cutoff functions of -energies on metric measure spaces
Meng Yang
For , and for a -energy on a volume doubling metric measure space, we provide several geometric and functional conditions for the validity of the cutoff Sobolev inequality.…
On singularity of -energy measures on metric measure spaces
Meng Yang
For , we prove that, for a -energy on a volume doubling metric measure space, the Poincaré inequality and the cutoff Sobolev inequality, both with -walk dimension stric…
-Poincaré inequalities and cutoff Sobolev inequalities on metric measure spaces
Meng Yang
For , we introduce the cutoff Sobolev inequality on general metric measure spaces, and prove that there exists a metric measure space endowed with a -energy that satisfies…
Hölder regularity of harmonic functions on metric measure spaces
Jin Gao, Meng Yang
We introduce a Hölder regularity condition for harmonic functions on metric measure spaces and prove that, under a slow volume regular condition and an upper heat kernel estimate,…
On the dichotomy of -walk dimensions on metric measure spaces
Meng Yang
On a volume doubling metric measure space endowed with a family of -energies such that the Poincaré inequality and the cutoff Sobolev inequality with -walk dimension …