Asymmetry of twisted convolution operators |
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Authors: | Anna Maria Mantero |
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Institution: | Università di Genova, Istituto di Matematica, Via L. B. Alberti 4, 16132 Genova, Italy |
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Abstract: | Let K be a distribution on 2. We denote by λ(K) the twisted convolution operator f → K × f defined by the formula K × f(x, y) = ∝∝ dudvK(x ? u, y ? v) f(u, v) exp(ixv ? iyu). We show that there exists K such that the operator λ(K) is bounded on Lp(R)2 for every p in (1, 2¦, but is unbounded on Lq(R)2 for every q > 2. |
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