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 L-mu(p),phi,phi) (G) over non-homogeneous spaces, where G subset of R-n is a bounded domain. Under assumption that functions phi and phi satisfy certain conditions, the authors prove that the Hardy-Littlewood maximal operator, fractional integral operators and theta-type Calderon-Zygmund operators are bounded on the non-homogeneous grand generalized Morrey space L-mu(p),phi,phi) (G). Moreover, the boundedness of commutator [b, T-theta(G)] which is generated by theta-type Calderon-Zygmund operator T-theta and b is an element of RBMO(mu) on spaces L-mu(p),phi,phi) (G) is also established.