Equivalent norms, Hardy-Littlewood-type theorems,and their applications  

作　　者：Shaolin Chen Hidetaka Hamada 

机构地区：[1]College of Mathematics and Statistics,Hengyang Normal University,Hengyang 421002,China [2]Faculty of Science and Engineering,Kyushu Sangyo University,Fukuoka 813-8503,Japan

出　　处：《Science China Mathematics》2025年第3期533-558,共26页中国科学(数学英文版)

基　　金：supported by National Natural Science Foundation of China (Grant No. 12071116);the Hunan Provincial Natural Science Foundation of China (Grant No. 2022JJ10001);the Key Projects of Hunan Provincial Department of Education (Grant No. 21A0429);the Double First-Class University Project of Hunan Province (Grant No. Xiangjiaotong [2018]469);the Science and Technology Plan Project of Hunan Province (Grant No. 2016TP1020);the Discipline Special Research Projects of Hengyang Normal University (Grant No. XKZX21002);supported by the Japan Society for the Promotion of Science KAKENHI (Grant No. JP22K03363)。

摘　　要：The primary goal of this paper is to develop methods for investigating equivalent norms and HardyLittlewood-type theorems on Lipschitz-type spaces of analytic and complex-valued harmonic functions. First,we provide characterizations of equivalent norms on these spaces. Furthermore, we establish Hardy-Littlewoodtype theorems for complex-valued harmonic functions. These results improve and extend the main findings of Dyakonov(1997) and Dyakonov(2005). Additionally, we apply the derived equivalent norms and HardyLittlewood-type theorems to the study of composition operators between Lipschitz-type spaces.

关 键 词：Lipschitz space equivalent norm harmonic function composition operator 

分 类 号：O174.5[理学—数学]