Weak Musielak–Orlicz Hardy spaces and applications |
| |
| Authors: | Yiyu Liang Dachun Yang Renjin Jiang |
| |
| Affiliation: | 1. +86 (0) 10 5880 5472+86 (0) 10 5880 5472;2. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, People's Republic of China;3. Current Address: Department of Mathematics, Beijing Jiaotong University, Beijing, People's Republic of China |
| |
| Abstract: | Let  satisfy that  , for any given  , is an Orlicz function and  is a Muckenhoupt  weight uniformly in  . In this article, the authors introduce the weak Musielak–Orlicz Hardy space  via the grand maximal function and then obtain its vertical or its non–tangential maximal function characterizations. The authors also establish other real‐variable characterizations of  , respectively, in terms of the atom, the molecule, the Lusin area function, the Littlewood–Paley g‐function or  ‐function. All these characterizations for weighted weak Hardy spaces  (namely,  and  with  and  ) are new and part of these characterizations even for weak Hardy spaces  (namely,  and  with  ) are also new. As an application, the boundedness of Calderón–Zygmund operators from  to  in the critical case is presented. |
| |
| Keywords: | Musielak– Orlicz function weak Musielak– Orlicz Hardy space maximal function atom molecule Littlewood– Paley operator Calderó n– Zygmund operator Primary: 42B30 Secondary: 42B20 42B25 42B35 |
|
|
