Boundedness of some operators on grand generalized Morrey spaces over non-homogeneous spaces

The aim of this paper is to obtain the boundedness of some operator on grand generalized Morrey space ${\mathcal{L}}_{\mu }^{p),\phi ,\varphi }(G)$ over non-homogeneous spaces, where $G\subset$ ${\mathbb{R}}^n$ is a bounded domain. Under assumption that functions $\phi$ and $\varphi$ satisfy certain conditions, the authors prove that the Hardy-Littlewood maximal operator, fractional integral operators and $\theta$-type Calderón-Zygmund operators are bounded on the non-homogeneous grand generalized Morrey space ${\mathcal{L}}_{\mu }^{p),\phi ,\varphi }(G)$. Moreover, the boundedness of commutator $[b,T_{\theta }^G]$ which is generated by $\theta$-type Calderón-Zygmund operator $T_{\theta }$ and $b\in \mathrm{R}\mathrm{B}\mathrm{M}\mathrm{O}(\mu )$ on spaces ${\mathcal{L}}_{\mu }^{p),\phi ,\varphi }(G)$ is also established.