| Lipschitz classes on local fields |
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| 引用本文： | Wei-yi SU~(1 ) Guo-xiang CHEN~2 1 Department of Mathematics,Nanjing University,Nanjing 210093,China, 2 Department of Mathematics,Nanjing Audit University,Nanjing 211815,China. Lipschitz classes on local fields[J]. 中国科学A辑(英文版), 2007, 50(7): 1005-1014. DOI: 10.1007/s11425-007-0058-8 |
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| 作者姓名： | Wei-yi SU~(1 ) Guo-xiang CHEN~2 1 Department of Mathematics Nanjing University Nanjing 210093 China 2 Department of Mathematics Nanjing Audit University Nanjing 211815 China |
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| 作者单位： | Wei-yi SU（Department of Mathematics, Nanjing University, Nanjing 210093, China） ;Guo-xiang CHEN（Department of Mathematics, Nanjing Audit University, Nanjing 211815, China ） ; |
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| 摘 要： | The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on the Euclidean space R~n and the local field K are compared,so that one may interpret the essential differences between the analyses on R~n and K.Finally,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m＜(ln 2/ln 3).
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Lipschitz classes on local fields |
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| Wei-yi Su,Guo-xiang Chen. Lipschitz classes on local fields[J]. Science in China(Mathematics), 2007, 50(7): 1005-1014. DOI: 10.1007/s11425-007-0058-8 |
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| Authors: | Wei-yi Su Guo-xiang Chen |
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| Affiliation: | 1. Department of Mathematics, Nanjing University, Nanjing 210093, China
2. Department of Mathematics, Nanjing Audit University, Nanjing 211815, China |
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| Abstract: | The Lipschitz class Lipα on a local field K is defined in this note, and the equivalent relationship between the Lipschitz class Lipα and the Holder type space C α (K) is proved. Then, those important characteristics on the Euclidean space R n and the local field K are compared, so that one may interpret the essential differences between the analyses on R n and K. Finally, the Cantor type fractal function ϑ(x) is showed in the Lipschitz class Lip (m, K), m < ln 2 / ln 3. This work supported by the National Natural Science Foundation of China (Grant No. 10571084) |
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| Keywords: | local field Holder type space Lipschitz class Cantor type fractal function |
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