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

Abstract

This paper aims to investigate the boundedness of some operators 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, we prove that Hardy-Littlewood maximal operator and $\theta$-type Calder\'{o}n-Zygmund operator are bounded on these spaces. Moreover, the boundedness of the commutator $[b, T_{\theta}]$ generated by the $\theta$-type Calderón-Zygmund operator and locally integrable function $b$ is also established. The results presented for grand generalized weighted Morrey spaces are also new even in the context of Euclidean domains.