| Lipschitz classes on local fields |
| |
| 作者姓名： | Wei-yi SU~ |
| |
| 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 ） ; |
| |
| 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).
|
Lipschitz classes on local fields |
| |
| Wei-yi SU.Lipschitz classes on local fields[J].Science in China(Mathematics),2007,50(7):1005-1014. |
| |
| Authors: | Wei-yi Su Guo-xiang Chen |
| |
| Institution: | 1. Department of Mathematics, Nanjing University, Nanjing 210093, China
2. Department of Mathematics, Nanjing Audit University, Nanjing 211815, China |
| |
| 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) |
| |
| Keywords: | local field Holder type space Lipschitz class Cantor type fractal function |
| 本文献已被 CNKI 万方数据 SpringerLink 等数据库收录！ |
|
