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Asymmetry of convolution operators on the Heisenberg group. (English) Zbl 0561.43004

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

MSC:

43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc.
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