Abstract
AbstractA linear and bounded operator T between Banach spaces X and Y has Fourier type 2 with respect to a locally compact abelian group G if there exists a constant c > 0 such that∥T$\hat f$∥2 ≤ c∥f∥2 holds for all X‐valued functions f ∈ LX2(G) where $\hat f$ is the Fourier transform of f. We show that any Fourier type 2 operator with respect to the classical groups has Fourier type 2 with respect to any locally compact abelian group. This generalizes previous special results for the Cantor group and for closed subgroups of ℝn. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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