## Abstract Presented is a general Fourier multiplier theorem for operator–valued multiplier functions on vector–valued Besov spaces where the required smoothness of the multiplier functions depends on the geometry of the underlying Banach space (specifically, its Fourier type). The main result cov
✦ LIBER ✦
Operator-valued Fourier multiplier theorems onLp-spaces on( mathbb{T}^d )
✍ Scribed by S. Bu; J.-M. Kim
- Publisher
- Springer
- Year
- 2004
- Tongue
- English
- Weight
- 128 KB
- Volume
- 82
- Category
- Article
- ISSN
- 0003-889X
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## Abstract Let __X__ be a Banach space. We show that each __m__ : ℝ \ {0} → __L__ (__X__ ) satisfying the Mikhlin condition sup~__x__ ≠0~(‖__m__ (__x__ )‖ + ‖__xm__ ′(__x__ )‖) < ∞ defines a Fourier multiplier on __B__ ^__s__^ ~__p,q__~ (ℝ; __X__ ) if and only if 1 < __p__ < ∞ and __X__ is isomorp