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On Function Spaces with Mixed Norms — A Survey

On Function Spaces with Mixed Norms — A Survey
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Year:    2021

Author:    Long Huang, Dachun Yang

Journal of Mathematical Study, Vol. 54 (2021), Iss. 3 : pp. 262–336

Abstract

The targets of this article are threefold. The first one is to give a survey on the recent developments of function spaces with mixed norms, including mixed Lebesgue spaces, iterated weak Lebesgue spaces, weak mixed-norm Lebesgue spaces and mixed Morrey spaces as well as anisotropic mixed-norm Hardy spaces. The second one is to provide a detailed proof for a useful inequality about mixed Lebesgue norms and the Hardy–Littlewood maximal operator and also to improve some known results on the maximal function characterizations of anisotropic mixed-norm Hardy spaces and the boundedness of Calderón–Zygmund operators from these anisotropic mixed-norm Hardy spaces to themselves or to mixed Lebesgue spaces. The last one is to correct some errors and seal some gaps existing in the known articles.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v54n3.21.03

Journal of Mathematical Study, Vol. 54 (2021), Iss. 3 : pp. 262–336

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    75

Keywords:    Mixed norm (weak) Lebesgue space Morrey space Hardy space maximal function Littlewood–Paley function Calderón–Zygmund operator.

Author Details

Long Huang

Dachun Yang

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    Wei, Mingquan | Su, Fangming | Sun, Lanyin

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    2024

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    Integral Operators in Grand Mixed-Normed Function Spaces

    Kokilashvili, Vakhtang | Meskhi, Alexander | Rafeiro, Humberto | Samko, Stefan

    2024

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  17. Intelligent Fractal-Based Image Analysis

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  20. A remark on the paper “Vector-valued operators with singular kernel and Triebel–Lizorkin block spaces with variable exponents” by Kwok Pun Ho

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    Tarigan, Muhammad O. I. P. | Gunadi, Reinhart | Hakim, Denny Ivanal |

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  34. Operator and Norm Inequalities and Related Topics

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    Kokilashvili, Vakhtang | Meskhi, Alexander

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    2022

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