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Strict local inclusion results between spaces of Fourier transforms

Strict local inclusion results between spaces of Fourier transforms

Let G denote a noncompact Hausdorff locally compact abelian group, Γ its character group, and write (L% l*)~ for the space of Fourier transforms of functions in the amalgam {L\l ι ).We show that for l^p<tf^°o the local inclusion loc (L 1 , l p )" c (L°°, 1 9 …