Grand Generalized Weighted Morrey Spaces for RD-Spaces

Abstract:

      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.