Heat kernel estimates, fractional Riesz transforms and applications on exterior domains
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913796385144832 |
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| author | Jiang, Renjin Shen, Tianjun Yang, Sibei Zhang, Houkun |
| author_facet | Jiang, Renjin Shen, Tianjun Yang, Sibei Zhang, Houkun |
| contents | In this paper, we derive sharp two side heat kernel estimate on exterior $C^{1,1}$ domains in the plane, and sharp upper heat kernel bound on exterior $C^{1,\mathrm{Dini}}$ domains in $\mathbb{R}^n$, $n\ge 2$. Estimates for Green's function and Riesz potentials on exterior domains in the plane are also presented. Based on the heat kernel estimates, we show the boundedness of the fractional Riesz transforms on exterior $C^{1,\mathrm{Dini}}$ domains in $\mathbb{R}^n$, $n\ge 2$. Some further applications to product and chain rules and nonlinear Schrödinger equation are also presented. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_11857 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Heat kernel estimates, fractional Riesz transforms and applications on exterior domains Jiang, Renjin Shen, Tianjun Yang, Sibei Zhang, Houkun Classical Analysis and ODEs Analysis of PDEs 42B20 In this paper, we derive sharp two side heat kernel estimate on exterior $C^{1,1}$ domains in the plane, and sharp upper heat kernel bound on exterior $C^{1,\mathrm{Dini}}$ domains in $\mathbb{R}^n$, $n\ge 2$. Estimates for Green's function and Riesz potentials on exterior domains in the plane are also presented. Based on the heat kernel estimates, we show the boundedness of the fractional Riesz transforms on exterior $C^{1,\mathrm{Dini}}$ domains in $\mathbb{R}^n$, $n\ge 2$. Some further applications to product and chain rules and nonlinear Schrödinger equation are also presented. |
| title | Heat kernel estimates, fractional Riesz transforms and applications on exterior domains |
| topic | Classical Analysis and ODEs Analysis of PDEs 42B20 |
| url | https://arxiv.org/abs/2504.11857 |