We present a functional analytic framework of some natural topologies on a given family of
spectral structures on Hilbert spaces, and study convergence of Riemannian manifolds and …

We prove the compactness of the imbedding of the Sobolev space W^1,2_0(Ω) into L^2(Ω)
for any relatively compact open subset Ω of an Alexandrov space. As a corollary, the …

Ischemia-reperfusion injury (IRI) results in increased rates of delayed graft function and early
graft loss. It has recently been reported that hydrogen sulfide (H 2 S) protects organ grafts …

In this paper, we investigate the structure of local space (in the broad sense) of (semi-)
Dirichlet forms and the functional calculus. In the theory of Dirichlet forms developed by M …

Restoration of oral and nasal function together with facial appearance is still challenging in
maxillary reconstruction. Use of a composite flap transfer merely to fill the defect results in …

We construct the 1, pfi-Sobolev spaces and energy functionals over Lp-maps between
metric spaces for pf 1 under the condition so-called strong measure contraction property of …

We prove a Jensen's inequality on p-uniformly convex space in terms of p-barycenters of
probability measures with (p-1)-th moment with p ∈ 1, ∞ under a geometric condition, which …

We establish the coincidence of two classes of Kato class measures in the framework of
symmetric Markov processes admitting upper and lower estimates of heat kernel under mild …

Stochastic calculus for symmetric Markov processes Page 1 The Annals of Probability 2008,
Vol. 36, No. 3, 931–970 DOI: 10.1214/07-AOP347 © Institute of Mathematical Statistics, 2008 …

Abstract Lu, Minguzzi, and Ohta introduced the notion of a lower N-weighted Ricci curvature
bound with ε-range and derived several comparison geometric estimates from a Laplacian …