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An Lp − Lq - Version of Morgan's Theorem Associated with Partial Differential Operators

Kamoun, Lotfi — 2005

Fractional Calculus and Applied Analysis

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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