Boundedness of some operators on grand generalized weighted Morrey spaces on RD-spaces

Abstract

The aim of this paper is to obtain the boundedness of some operator on grand generalized weighted Morrey spaces $\mathcal{L}^{p),\phi}_{\varphi}(\omega)$ over RD-spaces. Under assumption that functions $\varphi$ and $\phi$ satisfy certain conditions, the authors prove that Hardy-Littlewood maximal operator and $\theta$-type Calder\'{o}n-Zygmund operator are bounded on grand generalized weighted Morrey spaces $\mathcal{L}^{p),\phi}_{\varphi}(\omega)$. Moreover, the boundedness of commutator $[b,T_{\theta}]$ which is generated by $\theta$-type Calder\'{o}n-Zygmund operator $T_{\theta}$ and $b\in\mathrm{BMO}(\mu)$ on spaces $\mathcal{L}^{p),\phi}_{\varphi}(\omega)$ is also established. The results regarding the grand generalized weighted Morrey spaces is new even for domains of Euclidean spaces.