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arXiv 2203.04720math.FAmath.CA
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乘积广义混合Morrey空间上的多重次线性算子及其分解子

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

Mingquan Wei

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摘要：

本文研究了由多线性Calder{ó}n-Zygmund算子及其分解算子生成的一类多次线性算子$T_m$在乘积广义混合Morrey空间$M^{φ_1}_{\vec{q_1}}({\Bbb R}^n)\times\cdots\times M^{φ_m}_{\vec{q_m}}({\Bbb R}^n)$上的有界性.我们得到了$(φ_1,\cdots,φ_m,φ)$上保证算子$T_m$从$M^{φ_1}_{\vec{q_1}}({\Bbb R}^n)\times\cdots\times M^{φ_m}_{\vec{q_m}}({\Bbb R}^n)$到$M^φ_{\vec{q}}({\Bbb R}^n)$有界的充分条件.此外，还研究了$T^b_{m,i}$从$M^{φ_1}_{\vec{q_1}}({\Bbb R}^n)\times\cdots\times M^{φ_m}_{\vec{q_m}}({\Bbb R}^n)$到$M^φ_{\vec{q}}({\Bbb R}^n)$有界的充分条件.作为应用，我们得到了多重次线性极大算子、多重线性Calder{ó}n-Zygmund算子及其算子在乘积广义混合Morrey空间上的有界性.

英文摘要：

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.

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