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| 摘要: |
| 本文研究了一维直线上的奇异型Trudinger-Moser不等式.利用分数次Sobolev空间上函数的Green表示公式，得到了一类奇异型Trudinger-Moser不等式.进一步利用合适的测试函数序列验证了不等式中常数的最佳性.这一结果将高维空间上的奇异型Trudinger-Moser不等式推广到了一维情形. |
| 关键词: Trudinger-Moser不等式 分数次Sobolev空间 重排 最佳常数 |
| DOI： |
| 分类号:O178 |
| 基金项目: |
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| A FRACTIONAL SINGULAR TRUDINGER-MOSER INEQUALITY IN DIMENSION ONE |
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ZHU Mao-chun,LIU Jie
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| Abstract: |
| This paper is devoted to studying a singular fractional Trudinger-Moser inequality in dimension one. By the Green representation formula for functions in the fractional Sobolev spaces, we get a singular fractional Trudinger-Moser type inequality. Furthermore, by using a suitable test functions sequence, we can show that the constant in the inequality is optimal. This result extends the singular Trudinger-Moser inequality in the high-dimensional spaces to the space of dimension one. |
| Key words: Trudinger-Moser inequality fractional Sobolev space rearrangement optimal constant |
