Equivalence of operator norm for Hardy-Littlewood maximal operators and their truncated operators on Morrey spaces

doi:10.1007/s11464-020-0812-6

Front. Math. China

2020, Vol. 15

Issue (1) : 215-223 https://doi.org/10.1007/s11464-020-0812-6

RESEARCH ARTICLE

Equivalence of operator norm for Hardy-Littlewood maximal operators and their truncated operators on Morrey spaces

Xingsong ZHANG¹, Mingquan WEI²(

), Dunyan YAN¹, Qianjun HE³

¹. School of Mathematics, University of Chinese Academy of Sciences, Beijing 100049, China
². School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China
³. School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China

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Abstract

We will prove that for $1 < p < ∞$ and $0 < λ < n$ , the central Morrey norm of the truncated centered Hardy-Littlewood maximal operator $M γ c$ equals that of the centered Hardy-Littlewood maximal operator for all $0 < γ < + ∞$ . When p = 1 and $0 < λ < n$ , it turns out that the weak central Morrey norm of the truncated centered Hardy-Littlewood maximal operator $M γ c$ equals that of the centered Hardy-Littlewood maximal operator for all $0 < γ < + ∞$ . Moreover, the same results are true for the truncated uncentered Hardy-Littlewood maximal operator. Our work extends the previous results of Lebesgue spaces to Morrey spaces.

Keywords Hardy-Littlewood maximal function truncated Hardy-Littlewood maximal function Morrey norms weak Morrey norms

Corresponding Author(s): Mingquan WEI

Issue Date: 09 March 2020

Cite this article:

Xingsong ZHANG,Mingquan WEI,Dunyan YAN, et al. Equivalence of operator norm for Hardy-Littlewood maximal operators and their truncated operators on Morrey spaces[J]. Front. Math. China, 2020, 15(1): 215-223.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0812-6
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I1/215

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