Bochner-Riesz算子的多线性交换子的有界性

Boundedness for Multilinear Commutators of Bochner-Riesz Operator

中文关键词:  多线性交换子  Bochner-Riesz算子  Lipschitz函数  BMO空间.

英文关键词:multilinear commutators  Bochner-Riesz operator  Lipschitz function  BMO space.

中文摘要:

      本文考虑了Bochner-Riesz算子的多线性交换子的有界性，证明了由 Bochner-Riesz算子和Lipschitz函数生成的多线性交换子是从 $L^{p}({\Bbb R}^{n})$ 到$\dot{\wedge}_{(\beta-\frac{n}{p})}({\Bbb R}^{n})$ 和从 $L^{\frac{n}{\beta}}({\Bbb R}^{n})$ 到BMO$({\Bbb R}^{n})$上的有界性算子.

英文摘要:

      In this paper, the boundedness for the multilinear commutators of Bochner-Riesz operator is considered. We prove that the multilinear commutators generated by Bochner-Riesz operator and Lipschitz function are bounded from $L^{p}({\Bbb R}^{n})$ into $\dot{\wedge}_{(\beta-\frac{n}{p})}({\Bbb R}^{n})$ and from $L^{\frac{n}{\beta}}({\Bbb R}^{n})$ into BMO$({\Bbb R}^{n})$.