3 citations · 4 across the 6 of their papers we have counts for
8 papers
Riesz transform on eventually Gaussian local trees
Fabrice Baudoin, Aobo Chen, Li Chen
We study the Riesz transform on uniform local trees, metric measure spaces that are locally real trees and whose canonical Dirichlet form…
Riesz transforms on the Vicsek set
Fabrice Baudoin, Aobo Chen, Li Chen
We study Riesz and reverse Riesz inequalities for the fractional powers of the Laplacian on the unbounded Vicsek set. The space carries its Hausdorff measure . The gradient…
Walk dimension and vanishing curve modulus in metric measure spaces
Aobo Chen
On a regular local -Dirichlet space supporting a Poincaré inequality and a capacity upper bound, we characterize the existence of curve families of positive -modulus in terms…
Elliptic Harnack inequalities for mixed local and nonlocal -energy form on metric measure spaces
Aobo Chen, Zhenyu Yu
In the context of metric measure spaces, we introduce an axiomatic formulation of mixed local and nonlocal -energy forms. Within this framework, we use the Poincaré inequality,…
Spectral bounds and heat kernel upper estimates for Dirichlet forms
Aobo Chen, Zhenyu Yu
We use a Harnack-type inequality on exit times and spectral bounds to characterize upper bounds of the heat kernel associated with any regular Dirichlet form without killing part,…
Stability of heat kernel bounds under pointed Gromov--Hausdorff convergence
Aobo Chen
We construct a conservative and strongly local regular symmetric Dirichlet form on the pointed Gromov--Hausdorff limit space and demonstrate the stability of heat kernel estimates…
Besov-Lipschitz norm and -energy measure on scale-irregular Vicsek sets
Aobo Chen, Jin Gao, Zhenyu Yu +1
In this paper, we establish the existence of -energy norms and the corresponding -energy measures for scale-irregular Vicsek sets, which may lack self-similarity. We also inv…
Boundary Harnack principle on uniform domains
Aobo Chen
We present a proof of scale-invariant boundary Harnack principle for uniform domains when the underlying space satisfies a scale-invariant elliptic Harnack inequality. Our approach…