Some properties and interpolation theorems in weak Orlicz–Lorentz spaces

This paper is devoted to the studying of the weak Orlicz–Lorentz space ΛXφ,∞(w)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda_X^{\varphi, \infty}(w)$$\end{document}, which can be regarded as an extension of weak Orlicz space LXφ,∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_X^{\varphi, \infty}$$\end{document} and weak Lorentz space ΛXp,∞(w)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda_X^{p, \infty}(w)$$\end{document}. Results are obtained on the basic properties of convergence, normability and embedding relationships. Some interpolation theorems of operators are also given in the final part.