Integral operators on grand Morrey spaces

Abstract The main results of this paper give the boundedness of some integral operators on the grand Morrey spaces defined on the positive semi-axis. We obtain a general principle for the boundedness of integral operators on the grand Morrey spaces based on the mapping properties of the dilation operators on the grand Morrey spaces. As applications of our main results, we establish the boundedness of the Hardy operator, the adjoint Hardy operator and the Erdélyi–Kober fractional integrals on the grand Morrey spaces.