Frontiers of Mathematics in China >

2020 , Vol. 15 >Issue 1: 215 - 223

DOI: 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 ZHANG 1 ,
  • Mingquan WEI , 2 ,
  • Dunyan YAN 1 ,
  • Qianjun HE 3
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  • 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

Received date: 10 Oct 2019

Accepted date: 24 Dec 2019

Published date: 15 Feb 2020

Copyright

2020 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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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 Mγc 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 Mγc 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.

Key words： Hardy-Littlewood maximal function; truncated Hardy-Littlewood maximal function; Morrey norms; weak Morrey norms

Cite this article

Xingsong ZHANG , Mingquan WEI , Dunyan YAN , Qianjun HE . Equivalence of operator norm for Hardy-Littlewood maximal operators and their truncated operators on Morrey spaces[J]. Frontiers of Mathematics in China, 2020 , 15(1) : 215 -223 . DOI: 10.1007/s11464-020-0812-6

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