A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin–Triebel spaces with mixed norms
The article deals with a simplified proof of the Sobolev embedding theorem for Lizorkin–Triebel spaces (that contain the Lp-Sobolev spaces Hps as special cases). The method extends to a proof of the corresponding fact for general Lizorkin–Triebel spaces based on mixed Lp-norms. In this context a Nik...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2007/714905 |
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| _version_ | 1832560255252299776 |
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| author | Jon Johnsen Winfried Sickel |
| author_facet | Jon Johnsen Winfried Sickel |
| author_sort | Jon Johnsen |
| collection | DOAJ |
| description | The article deals with a simplified proof of the Sobolev embedding theorem for Lizorkin–Triebel spaces (that contain the Lp-Sobolev spaces Hps as special cases). The method extends to a proof of the corresponding fact for general Lizorkin–Triebel spaces based on mixed Lp-norms. In this context a Nikol' skij–Plancherel–Polya inequality for sequences of functions satisfying a geometric rectangle condition is proved. The results extend also to anisotropic spaces of the quasi-homogeneous type. |
| format | Article |
| id | doaj-art-867b215ff2e74a5481b752e82cd54c64 |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-867b215ff2e74a5481b752e82cd54c642025-02-03T01:28:00ZengWileyJournal of Function Spaces and Applications0972-68022007-01-015218319810.1155/2007/714905A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin–Triebel spaces with mixed normsJon Johnsen0Winfried Sickel1Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK–9220 Aalborg ǿst, DenmarkMathematics Department, Friedrich-Schiller-University Jena, Ernst-Abbe-Platz 2, D–07743 Jena, GermanyThe article deals with a simplified proof of the Sobolev embedding theorem for Lizorkin–Triebel spaces (that contain the Lp-Sobolev spaces Hps as special cases). The method extends to a proof of the corresponding fact for general Lizorkin–Triebel spaces based on mixed Lp-norms. In this context a Nikol' skij–Plancherel–Polya inequality for sequences of functions satisfying a geometric rectangle condition is proved. The results extend also to anisotropic spaces of the quasi-homogeneous type.http://dx.doi.org/10.1155/2007/714905 |
| spellingShingle | Jon Johnsen Winfried Sickel A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin–Triebel spaces with mixed norms Journal of Function Spaces and Applications |
| title | A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin–Triebel spaces with mixed norms |
| title_full | A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin–Triebel spaces with mixed norms |
| title_fullStr | A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin–Triebel spaces with mixed norms |
| title_full_unstemmed | A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin–Triebel spaces with mixed norms |
| title_short | A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin–Triebel spaces with mixed norms |
| title_sort | direct proof of sobolev embeddings for quasi homogeneous lizorkin triebel spaces with mixed norms |
| url | http://dx.doi.org/10.1155/2007/714905 |
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