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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.07395 |
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| _version_ | 1866909660403990528 |
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| author | Dafni, Galia Shaabani, Shahaboddin |
| author_facet | Dafni, Galia Shaabani, Shahaboddin |
| contents | Weak-type quasi-norms are defined using the mean oscillation or the mean of a function on dyadic cubes, providing discrete analogues and variants of the corresponding quasi-norms on the upper half-space previously considered in the literature. Comparing the resulting function spaces to known function spaces such as $\dot{W}^{1,p}(\rn)$, $\JNp$, $\Lp$ and weak-$\Lp$ gives new embeddings and characterizations of these spaces. Examples are provided to prove the sharpness of the results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07395 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Dyadic Approach to Weak Characterizations of Function Spaces Dafni, Galia Shaabani, Shahaboddin Functional Analysis Weak-type quasi-norms are defined using the mean oscillation or the mean of a function on dyadic cubes, providing discrete analogues and variants of the corresponding quasi-norms on the upper half-space previously considered in the literature. Comparing the resulting function spaces to known function spaces such as $\dot{W}^{1,p}(\rn)$, $\JNp$, $\Lp$ and weak-$\Lp$ gives new embeddings and characterizations of these spaces. Examples are provided to prove the sharpness of the results. |
| title | A Dyadic Approach to Weak Characterizations of Function Spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2409.07395 |