Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates

@article{AlonsoRuiz2020BesovCV,
  title={Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates},
  author={Patricia Alonso-Ruiz and Fabrice Baudoin and Li Chen and Luke G. Rogers and Nageswari Shanmugalingam and Alexander Teplyaev},
  journal={Calculus of Variations and Partial Differential Equations},
  year={2020},
  volume={59},
  pages={1-32}
}
We introduce the class of bounded variation (BV) functions in a general framework of strictly local Dirichlet spaces with doubling measure. Under the 2-Poincaré inequality and a weak Bakry–Émery curvature type condition, this BV class is identified with the heat semigroup based Besov class $$\mathbf {B}^{1,1/2}(X)$$ B 1 , 1 / 2 ( X ) that was introduced in our previous paper. Assuming furthermore a quasi Bakry–Émery curvature type condition, we identify the Sobolev class $$W^{1,p}(X)$$ W 1 , p… 
Equivalence of Besov spaces on p.c.f. self-similar sets
On p.c.f. self-similar sets, of which the walk dimensions of heat kernels are in general larger than 2, we find a sharp region where two classes of Besov spaces, the heat Besov spaces
Heat Kernels and Besov Spaces on Metric Measure Spaces
Let (M, ρ, μ) be a metric measure space satisfying the volume doubling condition. Assume also that ( M, ρ, μ) supports a heat kernel satisfying the upper and lower Gaussian bounds. We study the
RCD*(K,N) Spaces and the Geometry of Multi-Particle Schrödinger Semigroups
With $(X,\mathfrak{d},\mathfrak{m})$ an $\mathrm{RCD}(K,N)$ space for some $K\in\mathbf{R}$, $N\in [1,\infty)$, let $H$ be the self-adjoint Laplacian induced by the underlying Cheeger form. Given
BV functions and fractional Laplacians on Dirichlet spaces
We study $L^p$ Besov critical exponents and isoperimetric and Sobolev inequalities associated with fractional Laplacians on metric measure spaces. The main tool is the theory of heat semigroup based
Heat kernel analysis on diamond fractals
On (non-)singularity of energy measures under full off-diagonal heat kernel estimates
We show that for a strongly local, regular symmetric Dirichlet form over a complete, locally compact geodesic metric space, full off-diagonal heat kernel estimates with walk dimension strictly larger
BV Functions and Sets of Finite Perimeter on Configuration Spaces
This paper contributes to foundations of the geometric measure theory in the infinite dimensional setting of the configuration space over the Euclidean space R equipped with the Poisson measure π. We
$L^p$-Poincar\'e inequalities on nested fractals.
We prove on some nested fractals scale invariant $L^p$-Poincar\'e inequalities on metric balls in the range $1 \le p \le 2$. Our proof is based on the development of the local $L^p$-theory of
...
1
2
3
...

References

SHOWING 1-10 OF 200 REFERENCES
Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
This paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces $(X,\mathsf {d},\mathfrak {m})$. Our main results are: A general
Heat kernel characterisation of Besov-Lipschitz spaces on metric measure spaces
We give a heat-kernel characterisation of the Besov-Lipschitz spaces Lip (α, p, q)(X) on domains which support a Markovian kernel with appropriate exponential bounds. This extends former results of
Heat kernels on metric measure spaces and an application to semilinear elliptic equations
We consider a metric measure space (M, d, p) and a heat kernel p t (x,v) on M satisfying certain upper and lower estimates, which depend on two parameters a and β. We show that under additional mild
Geometry and Analysis of Dirichlet forms
Interpolation properties of Besov spaces defined on metric spaces
Let X = (X, d, μ)be a doubling metric measure space. For 0 < α < 1, 1 ≤p, q < ∞, we define semi‐norms When q = ∞ the usual change from integral to supremum is made in the definition. The Besov space
A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality
Let $$\mathbb M $$M be a smooth connected manifold endowed with a smooth measure $$\mu $$μ and a smooth locally subelliptic diffusion operator $$L$$L satisfying $$L1=0$$L1=0, and which is symmetric
Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and Lp-Liouville properties.
The basic object for the sequel is a fixed regul r Dirichlet form S with domain Q) ( } on a real Hubert space H = L(X, m). The underlying topological space X is a locally compact separable Hausdorff
Geometry and analysis of Dirichlet forms (II)
...
1
2
3
4
5
...