Grand variable Herz-Morrey-Hardy Spaces and applications to the boundedness of integral operators

In this paper, the concept of grand variable Herz-Morrey-Hardy spaces are introduced. We also establish the atomic characterization of these spaces. As an application the authors investigate the continuity of a few singular integral operators. We also obtain the boundedness of commutators of homogeneous fractional integrals and their Lipschitz estimate on these spaces by applying the characterization.