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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.12588 |
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| _version_ | 1866912235942576128 |
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| author | Ji, Un Cig Kim, Jae Hun |
| author_facet | Ji, Un Cig Kim, Jae Hun |
| contents | In this paper, we first prove that the kernel of convolution operator, corresponding the composition of pseudo-differential operator and evolution system associated with the symbol depending on time, satisfies the Hörmander's condition. Secondly, we prove that the convolution operator is a bounded linear operator from the Besov space on $\mathbb{R}^{d}$ into $L^{q}(\mathbb{R}^{d};V)$ for a Banach space $V$. Finally, by applying the Calderón-Zygmund theorem for vector-valued functions, we prove the Littlewood-Paley type inequality for evolution systems associated with pseudo-differential operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12588 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Littlewood-Paley Type Inequality for Evolution Systems Associated with Pseudo-Differential Operators Ji, Un Cig Kim, Jae Hun Analysis of PDEs 42B25, 42B37, 47G30 In this paper, we first prove that the kernel of convolution operator, corresponding the composition of pseudo-differential operator and evolution system associated with the symbol depending on time, satisfies the Hörmander's condition. Secondly, we prove that the convolution operator is a bounded linear operator from the Besov space on $\mathbb{R}^{d}$ into $L^{q}(\mathbb{R}^{d};V)$ for a Banach space $V$. Finally, by applying the Calderón-Zygmund theorem for vector-valued functions, we prove the Littlewood-Paley type inequality for evolution systems associated with pseudo-differential operators. |
| title | Littlewood-Paley Type Inequality for Evolution Systems Associated with Pseudo-Differential Operators |
| topic | Analysis of PDEs 42B25, 42B37, 47G30 |
| url | https://arxiv.org/abs/2502.12588 |