MORREY MEETS MUCKENHOUPT: A NOTE ON NAKAI'S GENERALIZED MORREY SPACES AND APPLICATIONS

In this paper, we introduce the generalized one-sided weighted Morrey spaces, which extend Nakai's generalized Morrey spaces to a wider function class, the one-sided Muckenhoupt weighted case. Morrey matching Muckenhoupt enables us to study both the weak and strong type boundedness of one-sided sublinear operators under certain size conditions. Moreover, we establish the boundedness of the Riemann-Liouville fractional integral and the compactness of the truncated Riemann-Liouville integral on these spaces. As an application, we obtain the existence and uniqueness of solutions to a Cauchy-type problem for fractional differential equations.