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Zongguang Liu

Publications and source records attributed to Zongguang Liu.

5 recordsLinked to original sources
arXiv2024

Anisotropic grand Herz type spaces with variable exponents and their applications

In this paper, we introduce some anisotropic grand Herz type spaces with variable exponents, including anisotropic grand Herz spaces, anisotropic grand Herz-Morrey spaces and anisotropic grand Herz-type Hardy spaces with variable exponents. We obtain some properties and characterizations of these spaces in terms of some decompositions. Using their decompositions, we obtain some boundedness on the anisotropic grand Herz type spaces with variable exponents for some singular integral operators.

math.FA↗
arXiv2018

Atomic Characterizations of Hardy Spaces Associated to Schrödinger Type Operators

In this article, the authors consider the Schrödinger type operator $L:=-{\rm div}(A\nabla)+V$ on $\mathbb{R}^n$ with $n\geq 3$, where the matrix $A$ is symmetric and satisfies uniformly elliptic condition and the nonnegative potential $V$ belongs to the reverse Hölder class $RH_q(\mathbb{R}^n)$ with $q\in(n/2,\,\infty)$. Let $p(\cdot):\ \mathbb{R}^n\to(0,\,1]$ be a variable exponent function satisfying the globally $\log$-Hölder continuous condition. The authors introduce the variable Hardy space $H_L^{p(\cdot)}(\mathbb{R}^n)$ associated to $L$ and establish its atomic characterization. The atoms here are closer to the atoms of variable Hardy space $H^{p(\cdot)}(\mathbb{R}^n)$ in spirit, which further implies that $H^{p(\cdot)}(\mathbb{R}^n)$ is continuously embedded in $H_L^{p(\cdot)}(\mathbb{R}^n)$.

math.CA↗
arXiv2018

Some Estimates of Schrödinger Type Operators on Variable Lebesgue and Hardy Spaces

In this article, the authors consider the Schrödinger type operator $L:=-{\rm div}(A\nabla)+V$ on $\mathbb{R}^n$ with $n\geq 3$, where the matrix $A$ satisfies uniformly elliptic condition and the nonnegative potential $V$ belongs to the reverse Hölder class $RH_q(\mathbb{R}^n)$ with $q\in(n/2,\,\infty)$. Let $p(\cdot):\ \mathbb{R}^n\to(0,\,\infty)$ be a variable exponent function satisfying the globally $\log$-Hölder continuous condition. When $p(\cdot):\ \mathbb{R}^n\to(1,\,\infty)$, the authors prove that the operators $VL^{-1}$, $V^{1/2}\nabla L^{-1}$ and $\nabla^2L^{-1}$ are bounded on variable Lebesgue space $L^{p(\cdot)}(\mathbb{R}^n)$. When $p(\cdot):\ \mathbb{R}^n\to(0,\,1]$, the authors introduce the variable Hardy space $H_L^{p(\cdot)}(\mathbb{R}^n)$, associated to $L$, and show that $VL^{-1}$, $V^{1/2}\nabla L^{-1}$ and $\nabla^2L^{-1}$ are bounded from $H_L^{p(\cdot)}(\mathbb{R}^n)$ to $L^{p(\cdot)}(\mathbb{R}^n)$.

math.CA↗
arXiv2017

Central BMO spaces with variable exponent

In this paper, the central BMO spaces with variable exponent are introduced. As an application, we characterize these spaces by the boundedness of commutators of Hardy operator and its dual operator on variable Lebesgue spaces. The boundedness of vector-valued commutators on Herz spaces with variable exponent are also considered.

math.FA↗