一类Marcinkiewicz积分交换子的Hardy空间估计

The Hardy Spaces Estimates for the Commutator of Marcinkiewicz Integral

中文关键词:  交换子  Marcinkiewicz积分  Lipschitz空间  Hardy空间  Herz型Hardy空间.

英文关键词:commutator  Marcinkiewicz integral  Lipschitz space  Hardy space  Herz type Hardy space.

中文摘要:

      本文证明了某种关于核的对数型Lipschitz条件下,带零次齐次核的Marcinkiewicz积分交换子是$(H^1,L^{n/(n-\beta)})$和$(H\dot{K}^{n(1-1/q_1),p}_{q_1},\dot{K}^{n(1-1/q_1),p}_{q_2})$型有界算子.

英文摘要:

      In this paper, we obtain the $(H^1,L^{n/(n-\beta)})$ and $(H\dot{K}^{n(1-1/q_1),p}_{q_1},\dot{K}^{n(1-1/q_1),p}_{q_2})$ type estimates for the commutator of Marcinkiewicz integral with the kernel satisfying the logarithmic type Lipschitz conditions.