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, Mg+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {M}}<^>{+}_{g}$$\end{document} on one-sided weighted like Morrey space, Mp,alpha+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M<^>{+}_{p,\alpha }$$\end{document} 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.