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.
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This work supported by the National Natural Science Foundation of China (Grant No. 10571084)
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Su, Wy., Chen, Gx. Lipschitz classes on local fields. SCI CHINA SER A 50, 1005–1014 (2007). https://doi.org/10.1007/s11425-007-0058-8
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DOI: https://doi.org/10.1007/s11425-007-0058-8