Two weighted norm inequalities for generalized one-sided maximal function on one-sided weighted like Morrey space

In this article, we study the boundedness of generalized one-sided maximal function, \({\mathcal {M}}^{+}_{g}\) ${\mathcal{M}}_g^{+}$ on one-sided weighted like Morrey space, \(M^{+}_{p,\alpha }\) $M_{p,\alpha }^{+}$ for a pair of weights (u, v). We also discuss the Fefferman-Stein’s type weighted inequalities for generalized one-sided maximal function on the same space. Finally, as a corollary, we obtain the Fefferman-Stein’s type inequalities for generalized one-sided maximal function on one-sided weighted like Morrey space for a pair of weights.