## Abstract Given __μ__ > 1, 1 ≤ __p__≤¡∞, 1 ≤ __q__ ≤ ∞, and 0 < __s__ < __μ__ + $ 1 \over p $, we show that the mapping __F__~__μ__~ : __f__ ↦ |__f__|^__μ__^ maps the Besov pace __B__^__s__^~__p,q__~ (ℝ^__n__^) ∩ __L__^∞^(ℝ^__n__^) on itself.
On the Boundedness of Pseudo - Differential Operators on Weighted Besov - Triebel Spaces
✍ Scribed by Peter Dintelmann
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 409 KB
- Volume
- 183
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
An elementary straightforward proof for the boundedness of pseudo ‐ differential operators of the Hörmander class Ψ^μ^~I,δ~ on weighted Besov ‐ Triebel spaces is given using a discrete characterization of function spaces.
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