11 citations · 35 across the 12 of their papers we have counts for
13 papers
Equivalent characterizations of John and uniform domains in doubling metric spaces
Yaxiang Li, Yahui Sheng, Zhuang Wang
In this paper, we characterize John and uniform domains in doubling metric spaces. Specifically, we show that a locally quasiconvex domain in a doubling metric space is length John…
Boxing inequalities for relative fractional perimeter and fractional Poincaré-type inequalities on John domains with the BBM factor
Manzi Huang, Panu Lahti, Jiang Li +1
For and , we prove that for a given -John domain , the following Boxing inequality holds for every Lebesgue measurable…
Empowering Distributed Training with Sparsity-driven Data Synchronization
Zhuang Wang, Zhaozhuo Xu, Jingyi Xi +3
Distributed training is the de facto standard to scale up the training of deep learning models with multiple GPUs. Its performance bottleneck lies in communications for gradient sy…
Locally biHölder continuous mappings and their induced embeddings between Besov spaces
Manzi Huang, Xiantao Wang, Zhuang Wang +1
In this paper, we introduce a class of homeomorphisms between metric spaces, which are locally biHölder continuous mappings. Then an embedding result between Besov spaces induced b…
Borderline case of traces and extensions for weighted Sobolev spaces
Manzi Huang, Xiantao Wang, Zhuang Wang +1
In this paper, we study the traces and the extensions for weighted Sobolev spaces on upper half spaces when the weights reach to the borderline cases. We first give a full characte…
-harmonic mappings between metric spaces
Chang-Yu Guo, Manzi Huang, Zhuang Wang +1
In this paper, we solve the Dirichlet problem for Sobolev maps between singular metric spaces that extends the corresponding result of Guo and Wenger [Comm. Anal. Geom. 2020]. The…
Improved regularity of harmonic diffeomorphic extensions on quasihyperbolic domains
Zhuang Wang, Haiqing Xu
Let be a Jordan domain satisfying hyperbolic growth conditions. Assume that is a homeomorphism from the boundary of onto the uni…
Characterization of trace spaces on regular trees via dyadic norms
Zhuang Wang
In this paper, we study the traces of Orlicz-Sobolev spaces on a regular rooted tree. After giving a dyadic decomposition of the boundary of the regular tree, we present a characte…
Trace and density results on regular trees
Pekka Koskela, Khanh Ngoc Nguyen, Zhuang Wang
We give characterizations for the existence of traces for first order Sobolev spaces defined on regular trees.
Traces of Newton-Sobolev, Hajlasz-Sobolev and BV functions on metric spaces
Panu Lahti, Xining Li, Zhuang Wang
We study the boundary traces of Newton-Sobolev, Hajlasz-Sobolev, and BV (bounded variation) functions. Assuming less regularity of the domain than is usually done in the literature…
Dyadic norm Besov-type spaces as trace spaces on regular trees
Pekka Koskela, Zhuang Wang
In this paper, we study function spaces defined via dyadic energies on the boundaries of regular trees. We show that correct choices of dyadic energies result in Besov-type spaces…
Controlled diffeomorphic extension of homeomorphisms
Pekka Koskela, Zhuang Wang, Haiqing Xu
Let be an internal chord-arc Jordan domain and be a homeomorphism. We show that has finite dyadic energy if and only if has a diffeomo…
Traces of weighted function spaces: dyadic norms and Whitney extensions
Pekka Koskela, Tomás Soto, Zhuang Wang
The trace spaces of Sobolev spaces and related fractional smoothness spaces have been an active area of research since the work of Nikolskii, Aronszajn, Slobodetskii, Babich and Ga…