高维拟共形映射的Hardy和Bergman空间.pdf

目录

目录

摘要···················································································I

Abstract·················································································III

1研究背景及主要结果······························································1

2预备知识················································································7

2.1平面拟共形映射·····························································7

2.2-维空间拟共形映射······················································9

2.3重要引理·······································································12

3拟共形映射的Hardy和Bergman空间······································17

3.1拟共形映射的Hardy空间的平均导数刻画·······················17

3.2拟共形映射的Hardy空间的几何刻画······························18

3.3拟共形映射的Bergman空间的极大模刻画······················19

总结与展望···············································································21

参考文献···················································································27

致谢···················································································31

硕士学位期间主要研究成果·······················································33

贵州师范大学学位论文原创性声明············································35

贵州师范大学学位论文使用授权书············································35

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摘要

摘要

解析函数的Hardy和Bergman空间理论是复分析一个重要且十分

活跃的研究课题.对于解析函数的Hardy空间已经有了许多漂亮的结

果,那么拟共形映射作为解析映射的一个自然推广是否也具有丰富

的理论？Astala和Koskela