Fractional Sobolev embeddings and algebra property: A dyadic view
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913946429030400 |
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| author | Ruiz, Patricia Alonso Fragkiadaki, Valentia |
| author_facet | Ruiz, Patricia Alonso Fragkiadaki, Valentia |
| contents | This paper revisits classical fractional Sobolev embedding theorems and the algebra property of the fractional Sobolev space $H^s(\mathbb{R})$ by means of Haar functions and dyadic decompositions. The aim is to provide an alternative, hands-on approach without Fourier transform that may be transferred to settings where the latter is not available. Explicit counterexamples are constructed to show the failure of the algebra property in the low-regularity regime. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_12051 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional Sobolev embeddings and algebra property: A dyadic view Ruiz, Patricia Alonso Fragkiadaki, Valentia Classical Analysis and ODEs Functional Analysis 42B35, 26A33, 42A99 This paper revisits classical fractional Sobolev embedding theorems and the algebra property of the fractional Sobolev space $H^s(\mathbb{R})$ by means of Haar functions and dyadic decompositions. The aim is to provide an alternative, hands-on approach without Fourier transform that may be transferred to settings where the latter is not available. Explicit counterexamples are constructed to show the failure of the algebra property in the low-regularity regime. |
| title | Fractional Sobolev embeddings and algebra property: A dyadic view |
| topic | Classical Analysis and ODEs Functional Analysis 42B35, 26A33, 42A99 |
| url | https://arxiv.org/abs/2412.12051 |