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

15 pages