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| Autori principali: | , , |
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| Natura: | Preprint |
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2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2504.04127 |
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| _version_ | 1866908302793768960 |
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| author | Avetisyan, Zhirayr Karapetyants, Alexey Mirotin, Adolf |
| author_facet | Avetisyan, Zhirayr Karapetyants, Alexey Mirotin, Adolf |
| contents | In this paper, we consider a two-dimensional operator with an antisymmetric integral kernel, recently introduced by Z. Avetisyan and A. Karapetyants in connection to the study of general homogeneous operators. This is the unique two-dimensional operator that has an antisymmetric kernel homogeneous with respect to all orientation-preserving linear transformations of the plane. It is shown that the operator under consideration interacts naturally, both in Cartesian and polar coordinates, with projective tensor products of some classical functional spaces, such as Lebesgue, Hardy, and Hölder spaces; conditions for their boundedness as operators acting from these spaces to Banach lattices of measurable functions and estimates of their norms are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04127 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a unique two-dimensional integral operator homogeneous with respect to all orientation preserving linear transformations Avetisyan, Zhirayr Karapetyants, Alexey Mirotin, Adolf Functional Analysis 44A05, 44A15 In this paper, we consider a two-dimensional operator with an antisymmetric integral kernel, recently introduced by Z. Avetisyan and A. Karapetyants in connection to the study of general homogeneous operators. This is the unique two-dimensional operator that has an antisymmetric kernel homogeneous with respect to all orientation-preserving linear transformations of the plane. It is shown that the operator under consideration interacts naturally, both in Cartesian and polar coordinates, with projective tensor products of some classical functional spaces, such as Lebesgue, Hardy, and Hölder spaces; conditions for their boundedness as operators acting from these spaces to Banach lattices of measurable functions and estimates of their norms are given. |
| title | On a unique two-dimensional integral operator homogeneous with respect to all orientation preserving linear transformations |
| topic | Functional Analysis 44A05, 44A15 |
| url | https://arxiv.org/abs/2504.04127 |