Volume 36, Issue 4
A Survey on Some Anisotropic Hardy-Type Function Spaces

Anal. Theory Appl., 36 (2020), pp. 373-456.

Published online: 2020-12

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• Abstract

Let $A$ be a general expansive matrix on $\mathbb{R}^n$. The aims of this article are twofold. The first one is to give a survey on the recent developments of anisotropic Hardy-type function spaces on $\mathbb{R}^n$, including anisotropic Hardy–Lorentz spaces, anisotropic variable Hardy spaces and anisotropic variable Hardy–Lorentz spaces as well as anisotropic Musielak–Orlicz Hardy spaces. The second one is to correct some errors and seal some gaps existing in the known articles. Some unsolved problems are also presented.

• Keywords

Expansive matrix, (variable) Hardy space, (variable) Hardy–Lorentz space, Musielak–Orlicz Hardy space.

42B35, 42B30, 42B25, 46B70

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• TXT
@Article{ATA-36-373, author = {Jun and Liu and and 9744 and and Jun Liu and Dorothee and D. Haroske and and 9745 and and Dorothee D. Haroske and Dachun and Yang and and 9746 and and Dachun Yang}, title = {A Survey on Some Anisotropic Hardy-Type Function Spaces}, journal = {Analysis in Theory and Applications}, year = {2020}, volume = {36}, number = {4}, pages = {373--456}, abstract = {

Let $A$ be a general expansive matrix on $\mathbb{R}^n$. The aims of this article are twofold. The first one is to give a survey on the recent developments of anisotropic Hardy-type function spaces on $\mathbb{R}^n$, including anisotropic Hardy–Lorentz spaces, anisotropic variable Hardy spaces and anisotropic variable Hardy–Lorentz spaces as well as anisotropic Musielak–Orlicz Hardy spaces. The second one is to correct some errors and seal some gaps existing in the known articles. Some unsolved problems are also presented.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-SU10}, url = {http://global-sci.org/intro/article_detail/ata/18462.html} }
TY - JOUR T1 - A Survey on Some Anisotropic Hardy-Type Function Spaces AU - Liu , Jun AU - D. Haroske , Dorothee AU - Yang , Dachun JO - Analysis in Theory and Applications VL - 4 SP - 373 EP - 456 PY - 2020 DA - 2020/12 SN - 36 DO - http://doi.org/10.4208/ata.OA-SU10 UR - https://global-sci.org/intro/article_detail/ata/18462.html KW - Expansive matrix, (variable) Hardy space, (variable) Hardy–Lorentz space, Musielak–Orlicz Hardy space. AB -

Let $A$ be a general expansive matrix on $\mathbb{R}^n$. The aims of this article are twofold. The first one is to give a survey on the recent developments of anisotropic Hardy-type function spaces on $\mathbb{R}^n$, including anisotropic Hardy–Lorentz spaces, anisotropic variable Hardy spaces and anisotropic variable Hardy–Lorentz spaces as well as anisotropic Musielak–Orlicz Hardy spaces. The second one is to correct some errors and seal some gaps existing in the known articles. Some unsolved problems are also presented.

Jun Liu, Dorothee D. Haroske & Dachun Yang. (2020). A Survey on Some Anisotropic Hardy-Type Function Spaces. Analysis in Theory and Applications. 36 (4). 373-456. doi:10.4208/ata.OA-SU10
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