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

Zhang, Xingsong; Wei, Mingquan; Yan, Dunyan; He, Qianjun

doi:10.1007/s11464-020-0812-6

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2021

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Cited by 3 publications

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“…In addition, Zhang et al obtained the equivalence of operator norm between the truncated maximal function and the Hardy-Littlewood function on Morrey spaces in [8]:…”

Section: Introductionmentioning

confidence: 99%

The Equivalence of Operator Norm between the Hardy-Littlewood Maximal Function and Truncated Maximal Function on the Heisenberg Group

Zhang

2021

Journal of Function Spaces

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In this article, we define a kind of truncated maximal function on the Heisenberg space by M γ c f x = sup 0 < r < γ 1 / m B x , r ∫ B x , r f y d y . The equivalence of operator norm between the Hardy-Littlewood maximal function and the truncated maximal function on the Heisenberg group is obtained. More specifically, when 1 < p < ∞ , the L p norm and central Morrey norm of truncated maximal function are equal to those of the Hardy-Littlewood maximal function. When p = 1 , we get the equivalence of weak norm L 1 ⟶ L 1 , ∞ and M ̇ 1 , λ ⟶ W ̇ M 1 , λ . Those results are generalization of previous work on Euclid spaces.

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“…In addition, Zhang et al obtained the equivalence of operator norm between the truncated maximal function and the Hardy-Littlewood function on Morrey spaces in [8]:…”

Section: Introductionmentioning

confidence: 99%

The Equivalence of Operator Norm between the Hardy-Littlewood Maximal Function and Truncated Maximal Function on the Heisenberg Group

Zhang

2021

Journal of Function Spaces

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Fourier transform of anisotropic mixed-norm Hardy spaces

2021

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The sharp constant for truncated Hardy-Littlewood maximal inequality

Jia¹,

Shao²,

Wei³

et al. 2021

Preprint

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This paper focuses on the operator norm of the truncated Hardy-Littlewood maximal operator M b a and the strong truncated Hardy-Littlewood maximal operator M b a , respectively. We first present the L 1 -norm of M b a , and then the L 1 -norm of M b a is given. Our study may have some enlightening significance for the research on sharp constant for the classical Hardy-Littlewood maximal inequality.

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

Cited by 3 publications

References 6 publications

The Equivalence of Operator Norm between the Hardy-Littlewood Maximal Function and Truncated Maximal Function on the Heisenberg Group

The Equivalence of Operator Norm between the Hardy-Littlewood Maximal Function and Truncated Maximal Function on the Heisenberg Group

Fourier transform of anisotropic mixed-norm Hardy spaces

The sharp constant for truncated Hardy-Littlewood maximal inequality

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