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2000 Mathematics Subject Classification: 42B10, 43A32.
In this paper we take the strip KL = [0, +∞[×[−Lπ, Lπ], where L is a
positive integer. We consider, for a nonnegative real number α, two partial
differential operators D and Dα on ]0, +∞[×] − Lπ, Lπ[. We associate a
generalized Fourier transform Fα to the operators D and Dα. For this transform Fα, we establish an Lp − Lq − version of the Morgan's theorem under the assumption 1 ≤ p, q ≤ +∞.
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