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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832549058425651200 |
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| author | Cornelia Schneider |
| author_facet | Cornelia Schneider |
| author_sort | Cornelia Schneider |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b7215b43dff7448eb304be167a86456f |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-b7215b43dff7448eb304be167a86456f2025-02-03T06:12:18ZengWileyJournal of Function Spaces and Applications0972-68022009-01-017325128810.1155/2009/815676Spaces of Sobolev type with positive smoothness on ℝn, embeddings and growth envelopesCornelia Schneider0Cornelia Schneider, Universität Leipzig, PF 100920, D-04009 Leipzig, GermanyWe 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.http://dx.doi.org/10.1155/2009/815676 |
| spellingShingle | Cornelia Schneider Spaces of Sobolev type with positive smoothness on ℝn, embeddings and growth envelopes Journal of Function Spaces and Applications |
| title | Spaces of Sobolev type with positive smoothness on ℝn, embeddings and growth envelopes |
| title_full | Spaces of Sobolev type with positive smoothness on ℝn, embeddings and growth envelopes |
| title_fullStr | Spaces of Sobolev type with positive smoothness on ℝn, embeddings and growth envelopes |
| title_full_unstemmed | Spaces of Sobolev type with positive smoothness on ℝn, embeddings and growth envelopes |
| title_short | Spaces of Sobolev type with positive smoothness on ℝn, embeddings and growth envelopes |
| title_sort | spaces of sobolev type with positive smoothness on rn embeddings and growth envelopes |
| url | http://dx.doi.org/10.1155/2009/815676 |
| work_keys_str_mv | AT corneliaschneider spacesofsobolevtypewithpositivesmoothnessonrnembeddingsandgrowthenvelopes |