Classes of Fourier Multipliers and Besov-Nikolskij Spaces
β Scribed by Peter Dintelmann
- Publisher
- John Wiley and Sons
- Year
- 1995
- Tongue
- English
- Weight
- 586 KB
- Volume
- 173
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
β¦ Synopsis
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.
π SIMILAR VOLUMES
## Abstract Presented is a general Fourier multiplier theorem for operatorβvalued multiplier functions on vectorβvalued 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
## Abstract Let __X__ be a Banach space. We show that each __m__ : β \ {0} β __L__ (__X__ ) satisfying the Mikhlin condition sup~__x__ β 0~(β__m__ (__x__ )β + β__xm__ β²(__x__ )β) < β defines a Fourier multiplier on __B__ ^__s__^ ~__p,q__~ (β; __X__ ) if and only if 1 < __p__ < β and __X__ is isomorp
## Abstract Using Herz spaces, we obtain a sufficient condition for a bounded measurable function on β^__n__^ to be a Fourier multiplier on __H^p^~Ξ±~__ (β^__n__^ ) for 0 < __p__ < 1 and β__n__ < Ξ± β€ 0. Our result is sharp in a certain sense and generalizes a recent result obtained by Baernstein an