Spaces of Sobolev type with positive smoothness on ℝn, embeddings and growth envelopes
We characterize Triebel-Lizorkin spaces with positive smoothness on ℝn, obtained by different approaches. First we present three settings Fp,qs(ℝn),Fp,qs(ℝn),ℑp,qs(ℝn) associated to definitions by differences, Fourier-analytical methods and subatomic decompositions. We study their connections and di...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2009/815676 |
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| Summary: | We characterize Triebel-Lizorkin spaces with positive smoothness
on ℝn, obtained by different approaches. First we present three settings Fp,qs(ℝn),Fp,qs(ℝn),ℑp,qs(ℝn) associated to definitions by differences, Fourier-analytical
methods and subatomic decompositions. We study their connections and diversity,
as well as embeddings between these spaces and into Lorentz spaces. Secondly,
relying on previous results obtained for Besov spaces 𝔅p,qs(ℝn), we determine
their growth envelopes 𝔈G(Fp,qs(ℝn)) for 0≺p≺∞, 0≺q≤∞, s≻0, and
finally discuss some applications. |
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| ISSN: | 0972-6802 |