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.