A note on Hardy-Littlewood maximal operators

作者：Wei, Mingquan; Nie, Xudong; Wu, Di^*; Yan, Dunyan

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016, 2016(1): 21.

DOI：10.1186/s13660-016-0963-x

• Hardy-Littlewood maximal function
• truncated operator
• L-p norm
• weak (1,1) norm
• iterated Hardy-Littlewood maximal function

In this paper, we will prove that, for 1 < p < infinity, the L-p norm of the truncated centered Hardy-Littlewood maximal operator M-gamma(c) equals the norm of the centered Hardy-Littlewood maximal operator for all 0 < gamma < infinity. When p = 1, we also find that the weak (1, 1) norm of the truncated centered Hardy-Littlewood maximal operator M-gamma(c) equals the weak (1, 1) norm of the centered Hardy-Littlewood maximal operator for 0 < gamma < infinity. Moreover, the same is true for the truncated uncentered Hardy-Littlewood maximal operator. Finally, we investigate the properties of the iterated Hardy-Littlewood maximal function.

• 出版日期2016-1-20
• 单位中国科学院大学