Yuan Zhou

activity

20092022

most citedAnisotropic Singular Integrals in Product Spaces

27 citations · 119 across the 31 of their papers we have counts for

collaborators

Showing math.CAShow all

14 papers · 1 filter

math.CA2022

A Rademacher type theorem for Hamiltonians $H (x, p)$ and application to absolute minimizers

Jiayin Liu, Yuan Zhou

We establish a Rademacher type theorem involving Hamiltonians $H (x, p)$ under very weak conditions in both of Euclidean and Carnot-Carathéodory spaces. In particular, $H (x, p)$ is ass…

math.CA2013

Intrinsic Geometry and Analysis of Diffusion Processes and $L^{\infty}$ -Variational Problems

Pekka Koskela, Nageswari Shanmugalingam, Yuan Zhou

The aim of this paper is two-fold: First, we obtain a better understanding of the intrinsic distance of diffusion processes. Precisely, (i) for all $n \geq 1$ , the diffusion matrix $A…

math.CA2012★ 11 cited

Geometry and Analysis of Dirichlet forms

Pekka Koskela, Yuan Zhou

Let $E$ be a regular, strongly local Dirichlet form on $L^{2} (X, m)$ and $d$ the associated intrinsic distance. Assume that the topology induced by $d$ coincides with the…

math.CA2011★ 5 cited

Characterizations of Besov and Triebel-Lizorkin Spaces on Metric Measure Spaces

Amiran Gogatishvili, Pekka Koskela, Yuan Zhou

On a metric measure space satisfying the doubling property, we establish several optimal characterizations of Besov and Triebel-Lizorkin spaces, including a pointwise characterizat…

math.CA2010★ 7 cited

Pointwise Characterizations of Besov and Triebel-Lizorkin Spaces and Quasiconformal Mappings

Pekka Koskela, Dachun Yang, Yuan Zhou

In this paper, the authors characterize, in terms of pointwise inequalities, the classical Besov spaces $B ˙_{p, q}^{s}$ and Triebel-Lizorkin spaces $F ˙_{p, q}^{s}$ for all $s…

math.CA2010★ 2 cited

Criteria for Optimal Global Integrability of Hajłasz-Sobolev Functions

Yuan Zhou

The author establishes some geometric criteria for a domain of $R^{n}$ with $n \geq 2$ to support a $(p n / (n - p s), p)_{s}$ -Hajłasz-Sobolev-Poincaré imbedding with $s \in (0, 1]$ a…

math.CA2009★ 1 cited

A Characterization of Hajłasz-Sobolev and Triebel-Lizorkin Spaces via Grand Littlewood-Paley Functions

Pekka Koskela, Dachun Yang, Yuan Zhou

In this paper, we establish the equivalence between the Hajłasz-Sobolev spaces or classical Triebel-Lizorkin spaces and a class of grand Triebel-Lizorkin spaces on Euclidean spaces…

math.CA2009

Radial Maximal Function Characterizations of Hardy Spaces on RD-Spaces and Their Applications

Dachun Yang, Yuan Zhou

Let $X$ be an RD-space with $μ (X) = \infty$ , which means that $X$ is a space of homogeneous type in the sense of Coifman and Weiss and its measure ha…

math.CA2009

Boundedness of Sublinear Operators on Product Hardy Spaces and Its Application

Der-Chen Chang, Dachun Yang, Yuan Zhou

Let $p \in (0, 1]$ . In this paper, the authors prove that a sublinear operator $T$ (which is originally defined on smooth functions with compact support) can be extended as a bounded…

math.CA2009★ 27 cited

Anisotropic Singular Integrals in Product Spaces

Baode Li, Marcin Bownik, Dachun Yang +1

Let $A_{i}$ for $i = 1, 2$ be an expansive dilation, respectively, on $R^{n}$ and $R^{m}$ and $A \equiv (A_{1}, A_{2})$ . Denote by ${\mathcal A}_\infty(\rnm; \vec A)$ th…

math.CA2009★ 2 cited

New Properties of Besov and Triebel-Lizorkin Spaces on RD-Spaces

Dachun Yang, Yuan Zhou

An RD-space $X$ is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in $X$ . In th…

math.CA2009★ 15 cited

Localized Hardy Spaces $H^{1}$ Related to Admissible Functions on RD-Spaces and Applications to Schrödinger Operators

Dachun Yang, Yuan Zhou

Let $X$ be an RD-space, which means that $X$ is a space of homogenous type in the sense of Coifman and Weiss with the additional property that a reverse doubl…

math.CA2009★ 10 cited

Localized Morrey-Campanato Spaces on Metric Measure Spaces and Applications to Schrödinger Operators

Dachun Yang, Dongyong Yang, Yuan Zhou

Let $X$ be a space of homogeneous type in the sense of Coifman and Weiss and $D$ a collection of balls in $\cx$. The authors introduce the localized atomic Ha…

math.CA2009★ 1 cited

Weighted Anisotropic Product Hardy Spaces and Boundedness of Sublinear Operators

Marcin Bownik, Baode Li, Dachun Yang +1

Let $A_{1}$ and $A_{2}$ be expansive dilations, respectively, on $R^{n}$ and $R^{m}$ . Let $A \equiv (A_{1}, A_{2})$ and $A_{p} (A)$ be the class of product Mu…

A Rademacher type theorem for Hamiltonians H(x,p) and application to absolute minimizers

Intrinsic Geometry and Analysis of Diffusion Processes and L∞-Variational Problems

Geometry and Analysis of Dirichlet forms

Characterizations of Besov and Triebel-Lizorkin Spaces on Metric Measure Spaces

Pointwise Characterizations of Besov and Triebel-Lizorkin Spaces and Quasiconformal Mappings

Criteria for Optimal Global Integrability of Hajłasz-Sobolev Functions

A Characterization of Hajłasz-Sobolev and Triebel-Lizorkin Spaces via Grand Littlewood-Paley Functions

Radial Maximal Function Characterizations of Hardy Spaces on RD-Spaces and Their Applications

Boundedness of Sublinear Operators on Product Hardy Spaces and Its Application

Anisotropic Singular Integrals in Product Spaces

New Properties of Besov and Triebel-Lizorkin Spaces on RD-Spaces

Localized Hardy Spaces H1 Related to Admissible Functions on RD-Spaces and Applications to Schrödinger Operators

Localized Morrey-Campanato Spaces on Metric Measure Spaces and Applications to Schrödinger Operators

Weighted Anisotropic Product Hardy Spaces and Boundedness of Sublinear Operators

A Rademacher type theorem for Hamiltonians $H (x, p)$ and application to absolute minimizers

Intrinsic Geometry and Analysis of Diffusion Processes and $L^{\infty}$ -Variational Problems

Localized Hardy Spaces $H^{1}$ Related to Admissible Functions on RD-Spaces and Applications to Schrödinger Operators