论文标题
混合莫雷空间和应用的双重双重
The Köthe dual of mixed Morrey spaces and applications
论文作者
论文摘要
在本文中，我们研究了混合 - lebesgue空间的可分离和弱收敛性。此外，我们证明了块空间$ \ mathcal {b} _ {\ vec {p} \，'}^{p'_0}（\ mathbb {r}^n）$是混合Morrey Space的双重$ \ mathcal {m} _ {\ vec {p}}}^{p_0}（\ Mathbb {r}^n）$通过这些块空间的fatou属性。在块空间$ \ mathcal {b} _ {\ vec {p} \，'}^{p'_0}（\ mathbb {r}^n）$上，进一步获得了强大的木材最大函数的界限。作为应用程序，证明了$ bmo（\ mathbb {r}^n）$的特征通过分数积分运算符$i_α$在混合空间上的换向器以及块空间$ \ mathcal {b} _ {\ vec {\ vec {\ vec {p} {p} \，'}^^n}^^n}
In this paper, we study the separable and weak convergence of mixed-norm Lebesgue spaces. Furthermore, we prove that the block space $\mathcal{B}_{\vec{p}\,'}^{p'_0}(\mathbb{R}^n)$ is the Köthe dual of the mixed Morrey space $\mathcal{M}_{\vec{p}}^{p_0}(\mathbb{R}^n)$ by the Fatou property of these block spaces. The boundedness of the Hardy--Littlewood maximal function is further obtained on the block space $\mathcal{B}_{\vec{p}\,'}^{p'_0}(\mathbb{R}^n)$. As applications, the characterizations of $BMO(\mathbb{R}^n)$ via the commutators of the fractional integral operator $I_α$ on mixed Morrey spaces are proved as well as the block space $\mathcal{B}_{\vec{p}\,'}^{p'_0}(\mathbb{R}^n)$.
