Geodesic
An Lp − Lq - Version of Morgan's Theorem Associated with Partial Differential Operators
Fractional calculus and applied analysis, Tome 8 (2005) no. 3, pp. 299-312.

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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 ≤ +∞.
Keywords: Generalized Fourier Transform, Morgan's Theorem, 42B10, 43A32 
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     author = {Kamoun, Lotfi},
     title = {An {Lp} \ensuremath{-} {Lq} - {Version} of {Morgan's} {Theorem} {Associated} with {Partial} {Differential} {Operators}},
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Kamoun, Lotfi. An Lp − Lq - Version of Morgan's Theorem Associated with Partial Differential Operators. Fractional calculus and applied analysis, Tome 8 (2005) no. 3, pp. 299-312. http://geodesic.mathdoc.fr/item/FCAA_2005_8_3_a4/