2 citations · 2 across the 6 of their papers we have counts for
10 papers
Two-sided heat kernel bounds for -Liouville Brownian motion
Sebastian Andres, Naotaka Kajino, Konstantinos Kavvadias +1
Liouville Brownian motion (LBM) is the canonical diffusion process on a Liouville quantum gravity (LQG) surface. In this work, we establish upper and lower bounds for the heat kern…
Generalized Kac's moment formula for positive continuous additive functionals of Markov processes
Naotaka Kajino, Ryoichiro Noda
We establish a formula for moments of certain random variables involving positive continuous additive functionals (PCAFs) of standard processes which have absolutely continuous tra…
-Energy forms on fractals: recent progress
Naotaka Kajino, Ryosuke Shimizu
In this article, we survey recent progress on self-similar -energy forms on self-similar fractals, where . While for the notion of such forms coincides wit…
Contraction properties and differentiability of -energy forms with applications to nonlinear potential theory on self-similar sets
Naotaka Kajino, Ryosuke Shimizu
We introduce a new contraction property, which we call the generalized -contraction property, for -energy forms as generalizations of many well-known inequalities, such as $p…
Korevaar-Schoen -energy forms and associated -energy measures on fractals
Naotaka Kajino, Ryosuke Shimizu
We construct good -energy forms on metric measure spaces as pointwise subsequential limits of Besov-type -energy functionals under certain geometric/analytic conditions. Such…
On singularity of energy measures for symmetric diffusions with full off-diagonal heat kernel estimates II: Some borderline examples
Naotaka Kajino
We present a concrete family of fractals, which we call the (two-dimensional) thin scale irregular Sierpiński gaskets and each of which is equipped with a canonical strongly local…