论文标题
多 - 连续性操作员及其换向器在产品广义混合空间上
Multi-sublinear operators and their commutators on product generalized mixed Morrey spaces
论文作者
论文摘要
在本文中，我们研究了由多连通式calder {} n-zygmund操作员及其换向器$ t^{b} _ {m，i}〜（i = 1，\ cdots，m）$ t_m $ t_m $ $ t_m $的界限$ m^{φ_1} _ {\ vec {q_1}}}（{\ bbb r}^n）我们在$（φ_1，\ cdots，φ_m，φ）$上找到足够的条件，这些条件确保了操作员的界限$ m^{φ_1} _ {\ vec {q_1}}}} m^{φ_m} _ {\ vec {q_m}}}（{\ bbb r}^n）$ to $ m^φ_ {\ vec {q}}}（{\ bbb r}^n）$。此外，从$ m^{φ_1} _ {\ vec {q_1}}}（{\ bbb r}^n）\ times \ times \ cdots \ cdipes m^{φ_m} {φ_m} _____________________ {还研究了r}^n）$ to $ m^φ_{\ vec {q}}}（{\ bbb r}^n）$。作为应用，我们获得了多连通性最大运算符的界限，多线性calder {ó} n-zygmund操作员及其换向器在产品普遍的混合摩尔雷空间上。
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.
