| 郑神州,饶婕晟.Heisenberg群上弱拟正则映射正则性的自我改善[J].数学年刊A辑,2013,34(5):579~588 |
| Heisenberg群上弱拟正则映射正则性的自我改善 |
| Self-improving Regularity of Weakly Quasiregular Mappings in Heisenberg Group |
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| DOI： |
| 中文关键词: Heisenberg群, 弱拟正则映射, Hodge分解 |
| 英文关键词:Heisenberg group, Weakly quasiregular mappings, Hodge decomposition |
| 基金项目:国家自然科学基金 (No.11071012) |
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| 中文摘要: |
| 考虑定义在Heisenberg群上的弱拟正则映射其水平微商可积性的自我改善. 在广义水平微商可积指数低于第1层空间维数的情况下,
通过接触映射的Jacobian和广义水平微商Jacobian的关系, 建立了逆向H\"older不等式, 从而得到其可积指数的自我提升. |
| 英文摘要: |
| In this paper, a self-improving integrability of the horizontal derivatives for
weakly quasiregular mappings defined in Heisenberg group is studied. The authors establish
a reverse H¨older inequality of the horizontal derivatives due to the relationship between
Jacobian determinant of contact maps f? and the horizontal derivatives Hf?, so that the
integrability of horizontal derivatives is shown to have a self-improving effect. |
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