On Function Spaces with Mixed Norms — A Survey
By Long Huang, Dachun Yang. Journal of Mathematical Study, 2019
93 citations recorded by the source corpus.
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 Calder\'on--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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f7b6c84d01982f786a65d76d9a26d3481944204a
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In Applied Mathematics
- Dachun Yang
- Wen Yuan
- Yangyang Zhang
- Songbai Wang
- Der-Chen Chang
- Yoshihiro Sawano
- Jun Liu
- Ciqiang Zhuo
In Mathematical Physics
- Dachun Yang
- Wen Yuan
- Yangyang Zhang
- Songbai Wang
- Der-Chen Chang
- Yoshihiro Sawano
- Ciqiang Zhuo
- Jun Liu
Citations in the corpus
- Weak Hardy-type spaces associated with ball quasi-Banach function spaces I: Decompositions with applications to boundedness of Calderón-Zygmund operators (2019, background): “on spaces, including mixed-norm Morrey spaces, mixed-norm Hardy spaces, mixed-norm Besov spaces and mixed-norm Triebel– Lizorkin spaces, has rapidly been developed in recent years (see, for instance, [17, 28, 58, 38, 39, 40]). Observe that L~p(Rn) when ~p ∈ (0,∞]n is a ball quasi-Banach function spa”
- Littlewood-Paley Characterizations of Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces (2019, background): “Particularly, in order to meet the requirements arising in the study of the boundedness of operators, partial differential equations and some other analysis fields, the real-variable theory of mixed-norm function spaces, including mixed-norm Morrey spaces, mixed-norm Hardy spaces, mixed-norm Besov s”