Grand Generalized Weighted Morrey Spaces for RD-Spaces
Received:June 02, 2022  Revised:October 04, 2022
Key Words: RD-space   Hardy-Littlewood maximal operator   $\theta$-type Calder\'{o}n-Zygmund operator   grand generalized weighted Morrey space  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12201500), the Science Foundation for Youths of Gansu Province (Grant No.22JR5RA173) and the Young Teachers' Scientific Research Ability Promotion Project of Northwest Normal University (Grant No.NWNU-LKQN2020-07).
Author NameAffiliation
Guanghui LU College of Mathematics and Statistics, Northwest Normal University, Gansu 730070, P. R. China 
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      Let $(X,d,\mu)$ be an RD-space satisfying both the doubling condition in the sense of\\ Coifman and Weiss and the reverse doubling condition. In this setting, the author obtains the\\ definition of grand generalized weighted Morrey space on $(X,d,\mu)$, and also investigates some p-\\roperties of these spaces. As an application, the boundedness of the Hardy-Littlewood maximal operator and the $\theta$-type Calder\'{o}n-Zygmund operator on spaces $\mathcal{L}^{p),\varphi,\Phi}_{\omega}(X)$ is also obtained.
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