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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.02705 |
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| _version_ | 1866914970318405632 |
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| author | Drihem, Douadi |
| author_facet | Drihem, Douadi |
| contents | In this paper, we introduce a new family of function spaces of Besov and Triebel-Lizorkin type. We present the $φ$-transform characterization of these spaces in the sense of Frazier and Jawerth and we prove their Sobolev and Franke-Jewarth embeddings. Also, we establish the smooth atomic, molecular and wavelet decomposition of these function spaces. Characterizations by ball means of differences are given. Finally, we investigate a series of examples which play an important role in the study of function spaces of Besov-Triebel-Lizorkin type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02705 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lorentz Herz-type Besov-Triebel-Lizorkin spaces Drihem, Douadi Functional Analysis Primary: 42B25, 42B35, secondary: 46E35 In this paper, we introduce a new family of function spaces of Besov and Triebel-Lizorkin type. We present the $φ$-transform characterization of these spaces in the sense of Frazier and Jawerth and we prove their Sobolev and Franke-Jewarth embeddings. Also, we establish the smooth atomic, molecular and wavelet decomposition of these function spaces. Characterizations by ball means of differences are given. Finally, we investigate a series of examples which play an important role in the study of function spaces of Besov-Triebel-Lizorkin type. |
| title | Lorentz Herz-type Besov-Triebel-Lizorkin spaces |
| topic | Functional Analysis Primary: 42B25, 42B35, secondary: 46E35 |
| url | https://arxiv.org/abs/2406.02705 |