Maximal and generalized fractional integral operators in grand Morrey martingale spaces

Abstract

In the spirit of grand Morrey spaces and martingale Morrey spaces, we introduce grand Morrey martingale spaces. Doob’s maximal inequalities on these spaces are presented. Furthermore, we establish the boundedness of generalized fractional integrals as martingale transforms in this framework. At the end, applications to some special cases are provided as well.