论文标题
与某些各向异性混合-Norm HERZ空间及其应用相关的耐寒空间
Hardy Spaces Associated with Some Anisotropic Mixed-Norm Herz Spaces and Their Applications
论文作者
论文摘要
在本文中，我们介绍各向异性混合 - 核HERZ空间$ \ dot k _ {\ vec {q}，\ vec {a}}}^{α，p}（\ m mathbb r^n）$和$ k _ { r^n）$并研究这些空间的一些基本属性。此外，在空间$ \ dot k _ {\ dot k _ {\ dot k _ {\ vec {Q}，\ vec {a}} $ p}（a}}^$ p}（al}^n）上，建立了Calderón-Zygmund操作员和分数积分操作员及其换向器的界限问题，该理论建立了卢比亚的外推理论。 $ k _ {\ vec {q}，\ vec {a}}}^{α，p}（\ mathbb r^n）$。尤其是，也获得了各向异性混合 - - 纳尔兹空间的莱特伍德 - 帕利特征。随着各向异性混合 - 纳尔斯赫兹空间的概括，我们介绍各向异性混合 - 纳尔兹 - 赫尔兹 - hardy空间$ h \ dot k _ {\ vec {q}，\ vec {a}}}}^{a}}^{α{α，p}（ \ vec {a}}^{α，p}（\ mathbb r^n）$，在其上获得了原子分解和分子分解。此外，我们获得了古典Calderón-Zygmund操作员的界限。
In this paper, we introduce anisotropic mixed-norm Herz spaces $\dot K_{\vec{q}, \vec{a}}^{α, p}(\mathbb R^n)$ and $K_{\vec{q}, \vec{a}}^{α, p}(\mathbb R^n)$ and investigate some basic properties of those spaces. Furthermore, establishing the Rubio de Francia extrapolation theory, which resolves the boundedness problems of Calderón-Zygmund operators and fractional integral operator and their commutators, on the space $\dot K_{\vec{q}, \vec{a}}^{α, p}(\mathbb R^n)$ and the space $K_{\vec{q}, \vec{a}}^{α, p}(\mathbb R^n)$. Especially, the Littlewood-Paley characterizations of anisotropic mixed-norm Herz spaces also are gained. As the generalization of anisotropic mixed-norm Herz spaces, we introduce anisotropic mixed-norm Herz-Hardy spaces $H\dot K_{\vec{q}, \vec{a}}^{α, p}(\mathbb R^n)$ and $HK_{\vec{q}, \vec{a}}^{α, p}(\mathbb R^n)$, on which atomic decomposition and molecular decomposition are obtained. Moreover, we gain the boundedness of classical Calderón-Zygmund operators.
