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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.05997 |
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| _version_ | 1866917069498351616 |
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| author | Rotkevich, Aleksandr |
| author_facet | Rotkevich, Aleksandr |
| contents | We construct an example of a Lebesgue space with variable exponent on which Cauchy-Leray-Fantappiè operator associated with a complex ellipsoid is not bounded. This result extends previous counterexamples for the unit ball and demonstrates that the logarithmic continuity condition for the exponent function $p(\cdot)$ is sharp even for non-strictly convex domains. The proof is based on an explicit construction of test functions supported near points where the boundary fails to be strictly convex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05997 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An example of a space $L^{p(\cdot)}$ on which the Cauchy-Leray-Fantappiè operator for complex ellipsoid is not bounded Rotkevich, Aleksandr Complex Variables We construct an example of a Lebesgue space with variable exponent on which Cauchy-Leray-Fantappiè operator associated with a complex ellipsoid is not bounded. This result extends previous counterexamples for the unit ball and demonstrates that the logarithmic continuity condition for the exponent function $p(\cdot)$ is sharp even for non-strictly convex domains. The proof is based on an explicit construction of test functions supported near points where the boundary fails to be strictly convex. |
| title | An example of a space $L^{p(\cdot)}$ on which the Cauchy-Leray-Fantappiè operator for complex ellipsoid is not bounded |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2511.05997 |