On Function Spaces with Mixed Norms — A Survey

On Function Spaces with Mixed Norms — A Survey

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