Volume 54, Issue 3
On Function Spaces with Mixed Norms — A Survey

Long Huang & Dachun Yang

J. Math. Study, 54 (2021), pp. 262-336.

Published online: 2021-03

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  • 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.

  • AMS Subject Headings

42B35, 42B30, 42B25, 42B20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

longhuang@mail.bnu.edu.cn (Long Huang)

dcyang@bnu.edu.cn (Dachun Yang)

  • BibTex
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  • TXT
@Article{JMS-54-262, author = {Huang , Long and Yang , Dachun}, title = {On Function Spaces with Mixed Norms — A Survey}, journal = {Journal of Mathematical Study}, year = {2021}, volume = {54}, number = {3}, pages = {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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v54n3.21.03}, url = {http://global-sci.org/intro/article_detail/jms/18735.html} }
TY - JOUR T1 - On Function Spaces with Mixed Norms — A Survey AU - Huang , Long AU - Yang , Dachun JO - Journal of Mathematical Study VL - 3 SP - 262 EP - 336 PY - 2021 DA - 2021/03 SN - 54 DO - http://doi.org/10.4208/jms.v54n3.21.03 UR - https://global-sci.org/intro/article_detail/jms/18735.html KW - Mixed norm, (weak) Lebesgue space, Morrey space, Hardy space, maximal function, Littlewood–Paley function, Calderón–Zygmund operator. AB -

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.

LongHuang & DachunYang. (2021). On Function Spaces with Mixed Norms — A Survey. Journal of Mathematical Study. 54 (3). 262-336. doi:10.4208/jms.v54n3.21.03
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