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.