Complex interpolation of variable Morrey spaces

Abstract In this paper, we investigate the description of complex interpolation between variable Morrey spaces. We show that the first complex interpolation between variable Morrey spaces equals to certain closed subspaces of variable Morrey spaces. In addition, we prove that the second complex interpolation of variable Morrey spaces coincides with their intermediate spaces. Our proof uses the characterization of the Calderón product between variable Morrey spaces. Our results cover complex interpolation of variable Lebesgue spaces and complex interpolation of (classical) Morrey spaces.