arXiv subjects

Mingquan Wei

Publications and source records attributed to Mingquan Wei.

8 recordsLinked to original sources

arXiv2025

Herz-Type Hardy Spaces Associated with Ball Quasi-Banach Function Spaces

Let $X$ be a ball quasi-Banach function space, $α\in \mathbb{R}$ and $q\in(0,\infty)$. In this paper, the authors first introduce the Herz-type Hardy space $\mathcal{H\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$, which is defined via the non-tangential grand maximal function. Under some mild assumptions on $X$, the authors establish the atomic decompositions of $\mathcal{H\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$. As an application, the authors obtain the boundedness of certain sublinear operators from $\mathcal{H\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$ to $\mathcal{\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$, where $\mathcal{\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$ denotes the Herz-type space associated with ball quasi-Banach function space $X$. Finally, the authors apply these results to three concrete function spaces: Herz-type Hardy spaces with variable exponent, mixed Herz-Hardy spaces and Orlicz-Herz Hardy spaces, which belong to the family of Herz-type Hardy spaces associated with ball quasi-Banach function spaces.

math.FA↗

arXiv2022

Operators on Herz-type spaces associated with ball quasi-Banach function spaces

Let $α\in{\Bbb R}$, $0<p<\infty$ and $X$ be a ball quasi-Banach function space on ${\Bbb R}^n$. In this article, we introduce the Herz-type space $\dot{K}^{α,p}_X({\Bbb R}^n)$ associated with $X$. We identify the dual space of $\dot{K}^{α,p}_X({\Bbb R}^n)$, by which the boundedness of Hardy-Littlewood maximal operator on $\dot{K}^{α,p}_X({\Bbb R}^n)$ is proved. By using the extrapolation theorem on ball quasi-Banach function spaces, we establish the extrapolation theorem on Herz-type spaces associated with ball quasi-Banach function spaces. Applying our extrapolation theorem, the boundedness of singular integral operators with rough kernels and their commutators, parametric Marcinkiewicz integrals, and oscillatory singular integral operators on $\dot{K}^{α,p}_X({\Bbb R}^n)$ is obtained. As examples, we give some concrete function spaces which are members of Herz-type spaces associated with ball quasi-Banach function spaces.

math.CA↗

arXiv2022

Sharp bounds for Hardy-type operators on mixed radial-angular spaces

In this paper, by using the rotation method, we calculate that the sharp bound for $n$-dimensional Hardy operator $\mathcal{H}$ on mixed radial-angular spaces. Furthermore, we also obtain the sharp bound for $n$-dimensional fractional Hardy operator $\mathcal{H}_β$ from $L^p_{|x|}L_θ^{\bar{p}}({\Bbb R}^n)$ to $L^q_{|x|}L_θ^{\bar{q}}({\Bbb R}^n)$, where $0<β<n$, $1<p,q,\bar{p},\bar{q}<\infty$ and $1/p-1/q=β/n$. By using duality, the corresponding results for the dual operators $\mathcal{H}^*$ and $\mathcal{H}^*_β$ are also established. In addition, the sharp weak-type estimate for $\mathcal{H}$ is also considered.

math.CA↗

arXiv2022

Characterizations of Mixed Herz-Hardy Spaces and their Applications

The purpose of this paper is to introduce and investigate some basic properties of mixed homogeneous Herz-Hardy spaces $H\dot{K}_{\vec{p}}^{α, q}(\mathbb{R}^n)$ and mixed non-homogeneous Herz-Hardy spaces $HK_{\vec{p}}^{α, q}(\mathbb{R}^n)$. Furthermore, we establish the atom and molecular decompositions for $H\dot{K}_{\vec{p}}^{α, q}(\mathbb{R}^n)$ and $HK_{\vec{p}}^{α, q}(\mathbb{R}^n)$, by which the boundedness for a wide class of sublinear operators on mixed Herz-Hardy spaces is obtained. As a byproduct, the dual spaces of mixed homogeneous Herz-Hardy spaces are deduced.

math.FA↗

arXiv2022

Multi-sublinear operators and their commutators on product generalized mixed Morrey spaces

In this paper, we study the boundedness for a large class of multi-sublinear operators $T_m$ generated by multilinear Calder{ó}n-Zygmund operators and their commutators $T^{b}_{m,i}~(i=1,\cdots,m)$ on the product generalized mixed Morrey spaces $M^{φ_1}_{\vec{q_1}}({\Bbb R}^n)\times\cdots\times M^{φ_m}_{\vec{q_m}}({\Bbb R}^n)$. We find the sufficient conditions on $(φ_1,\cdots,φ_m,φ)$ which ensure the boundedness of the operator $T_m$ from $M^{φ_1}_{\vec{q_1}}({\Bbb R}^n)\times\cdots\times M^{φ_m}_{\vec{q_m}}({\Bbb R}^n)$ to $M^φ_{\vec{q}}({\Bbb R}^n)$. Moreover, the sufficient conditions for the boundeness of $T^b_{m,i}$ from $M^{φ_1}_{\vec{q_1}}({\Bbb R}^n)\times\cdots\times M^{φ_m}_{\vec{q_m}}({\Bbb R}^n)$ to $M^φ_{\vec{q}}({\Bbb R}^n)$ are also studied. As applications, we obtain the boundedness for the multi-sublinear maximal operator, the multilinear Calder{ó}n-Zygmund operator and their commutators on product generalzied mixed Morrey spaces.

math.FA↗

arXiv2021

Boundedness criterion for sublinear operators and commutators on generalized mixed Morrey spaces

In this paper, the author studies the boundedness for a large class of sublinear operator $T_α, α\in[0,n)$ generated by Calder{ó}n-Zygmund operators ($α=0$) and generated by fractional integral operator ($α>0$) on generalized mixed Morrey spaces $M^φ_{\vec{q}}(\Bbb R^n)$. Moreover, the boundeness for the commutators of $T_α, α\in[0,n)$ on generalized mixed Morrey spaces $M^φ_{\vec{q}}(\Bbb R^n)$ is also studied. As applications, we obtain the boundedness for Hardy-Littlewood maximal operator, Calderón-Zygmund singular integral operators, fractional integral operator, fractional maximal operator and their commutators on generalzied mixed Morrey spaces.

math.FA↗

arXiv2021

The sharp constant for truncated Hardy-Littlewood maximal inequality

This paper focuses on the operator norm of the truncated Hardy-Littlewood maximal operator $M^b_a$ and the strong truncated Hardy-Littlewood maximal operator $\tilde{M}^{\boldsymbol{b}}_{\boldsymbol{a}}$, respectively. We first present the $L^1$-norm of $M^b_a$, and then the $L^1$-norm of $\tilde{M}^{\boldsymbol{b}}_{\boldsymbol{a}}$ is given. Our study may have some enlightening significance for the research on sharp constant for the classical Hardy-Littlewood maximal inequality.

math.CA↗

arXiv2019

Weighted estimates for bilinear fractional integral operators and their commutators on Morrey spaces

This paper mainly dedicates to prove a plethora of weighted estimates on Morrey spaces for bilinear fractional integral operators and their general commutators with BMO functions of the form $$B_α(f,g)(x)=\int_{\mathbb{R}^{n}}\frac{f(x-y)g(x+y)}{|y|^{n-α}}dy,\qquad 0<α<n.$$ We also prove some maximal function control theorems for these operators, that is, the weighted Morrey norm is bounded by the weighted Morrey norm of a natural maximal operator when the weight belongs to $A_{\infty}$. As a corollary, some new weighted estimates for the bilinear maximal function associated to the bilinear Hilbert transform are obtained. Furthermore, we formulate a bilinear version of Stein-Weiss inequality on Morrey spaces for fractional integrals.

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