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On the Fourier-Coefficients of Vector-Valued Functions

✍ Scribed by Hermann König

Publisher
John Wiley and Sons
Year
1991
Tongue
English
Weight
522 KB
Volume
152
Category
Article
ISSN
0025-584X

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✦ Synopsis

We study the decay of the FOURIER-coefficients of vector-valued functions F :T --+ X, X a BANAFH space. Differentiable functions f generally have absolutely sumrnable FOURIER-coefficients, 1 Ilf(n)ll < 00, iff X is K-convex. More precise statements on the decay of Ilf(n)ll for regular functions fcan be given if X has FOURIER-type p. Iff belongs to the BESOV space B:,(X), the sequence (Ilf(n)ll) belongs to the LORENTZ sequence space lZ," with -= A + . This result is the best possible in the vector-valued case and generalizes the well-known scalar results.

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