On Fourier multipliers between Besov spaces with 0
โ Scribed by Peter Dintelmann
- Book ID
- 112650046
- Publisher
- Springer
- Year
- 1996
- Tongue
- English
- Weight
- 419 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0133-3852
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract Let __X__ be a Banach space. We show that each __m__ : โ \ {0} โ __L__ (__X__ ) satisfying the Mikhlin condition sup~__x__ โ 0~(โ__m__ (__x__ )โ + โ__xm__ โฒ(__x__ )โ) < โ defines a Fourier multiplier on __B__ ^__s__^ ~__p,q__~ (โ; __X__ ) if and only if 1 < __p__ < โ and __X__ is isomorp
We present a discrete characterization of Besov and Triebel spaces which is used to determine various classes Fourier multipliers for these spaces. In particular, results of R. Johnson are recovered.
## Abstract Presented is a general Fourier multiplier theorem for operatorโvalued multiplier functions on vectorโvalued 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