On a general concept of a Hausdorff-type operator
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911918750433280 |
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| author | Mirotin, A. R. |
| author_facet | Mirotin, A. R. |
| contents | A unified approach to the concept of a Hausdorff operator is proposed in such a way that a number of classical and new operators feet into the given definition. Conditions are given for the boundedness of the operators under consideration in $L^p$ and in the atomic Hardy space $H^1$, and their regularity property is investigated.
Examples are considered. The author hopes that this approach will allow one to unify the study of a lot of extensions and analogs of the classical Hausdorff operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_02388 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On a general concept of a Hausdorff-type operator Mirotin, A. R. Functional Analysis 47B38 (Primary), 47B15, 46E30 (Secondary) A unified approach to the concept of a Hausdorff operator is proposed in such a way that a number of classical and new operators feet into the given definition. Conditions are given for the boundedness of the operators under consideration in $L^p$ and in the atomic Hardy space $H^1$, and their regularity property is investigated. Examples are considered. The author hopes that this approach will allow one to unify the study of a lot of extensions and analogs of the classical Hausdorff operator. |
| title | On a general concept of a Hausdorff-type operator |
| topic | Functional Analysis 47B38 (Primary), 47B15, 46E30 (Secondary) |
| url | https://arxiv.org/abs/2308.02388 |