Multipliers on Besov spaces
✍ Scribed by A. B. Gulisashvili
- Publisher
- Springer US
- Year
- 1985
- Tongue
- English
- Weight
- 547 KB
- Volume
- 31
- Category
- Article
- ISSN
- 1573-8795
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📜 SIMILAR VOLUMES
## 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
## 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
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 The boundedness of singular convolution operators __f__ ↦ __k__ ∗︁ __f__ is studied on Besov spaces of vector‐valued functions, the kernel __k__ taking values in ℒ︁(__X__ , __Y__ ). The main result is a Hörmander‐type theorem giving sufficient conditions for the boundedness of such an