Abstract
Let K be a distribution on R 2. We denote by λ( K) the twisted convolution operator f → K × f defined by the formula K × f( x, y) = ∝∝ du dv K( 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 L p ( R) 2 for every p in (1, 2¦, but is unbounded on L q ( R) 2 for every q > 2.
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