Mantero, Anna Maria Asymmetry of convolution operators on the Heisenberg group. (English) Zbl 0561.43004 Boll. Unione Mat. Ital., VI. Ser., A 4, 19-27 (1985). The author proves that on the 3-dimensional Heisenberg group G there is a convolution operator T which is bounded on \(L^ p(G)\) for all p in (1,2] and for no p in (2,\(\infty]\). The idea is to lift the analogous result for twisted convolution operators on \({\mathbb{C}}\), proved by the author [J. Functional Anal. 47, 7-25 (1982; Zbl 0533.43007)] to G, using techniques of J.-Ph. Anker and A. Derighetti [Bull. Sci. Math., II. Sér. 107, 3-23 (1983; Zbl 0522.43003)]. Reviewer: M.Cowling Cited in 1 Document MSC: 43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc. Keywords:3-dimensional Heisenberg; convolution operator; \(L^ p(G)\) Citations:Zbl 0533.43007; Zbl 0522.43003 PDFBibTeX XMLCite \textit{A. M. Mantero}, Boll. Unione Mat. Ital., VI. Ser., A 4, 19--27 (1985; Zbl 0561.43004)