本征平方函数在极大变指数Herz空间上的有界性

Boundedness of the Intrinsic Square Function on Grand Variable Herz Spaces

中文关键词:  本征平方函数  交换子  变指数  极大空间  Herz空间

英文关键词:the intrinsic square function  commutator  variable exponent  grand space  Herz space

中文摘要:

      我们证明了本征平方函数及其交换子在Herz空间$\dot{K}_{q(\cdot)}^{\alpha(\cdot), p),\theta}({\Bbb{R}}^n)$空间上的有界性,其中$\alpha$, $q$均为变指数。当$\alpha(\cdot)\equiv \alpha$为常数时,所得结果也是新的.

英文摘要:

      We prove that the intrinsic square function and its commutator are bounded on the Herz space $\dot{K}_{q(\cdot)}^{\alpha(\cdot), p),\theta}({\Bbb{R}}^n)$, where the exponents $\alpha$ and $q$ are variable. The results are still new even when $\alpha(\cdot)\equiv \alpha$ is constant.