Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-Multipliers Sensitive to the Group Structure on Nilpotent Lie Groups

We propose new sufficient conditions for Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-multipliers on homogeneous nilpotent groups. The multipliers generalise the flag multipliers of Nagel–Ricci–Stein–Wainger, but the approach and the techniques applied are entirely different. Our multipliers are better adapted to the specific commutation rules on the Lie algebra of the given group. The proofs are based on a new symbolic calculus fashioned after Hörmander. We also take advantage of the Cotlar–Stein lemma, and the Littlewood–Paley theory in the spirit of Duoandikoetxea–Rubio de Francia.