## Fractional differentiation and Lipschitz spaces on local fields

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- by C. W. Onneweer
- Trans. Amer. Math. Soc.
**258**(1980), 155-165 - DOI: https://doi.org/10.1090/S0002-9947-1980-0554325-1
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## Abstract:

In this paper we continue our study of differentiation on a local field**K**. We define strong derivatives of fractional order $\alpha > 0$ for functions in ${L_r}(\textbf {K})$, $1 \leqslant r < \infty$. After establishing a number of basic properties for such derivatives we prove that the spaces of Bessel potentials on

**K**are equal to the spaces of strongly ${L_r}(\textbf {K})$-differentiable functions of order $\alpha > 0$ when $1 \leqslant r \leqslant 2$. We then focus our attention on the relationship between these spaces and the generalized Lipschitz spaces over

**K**. Among others, we prove an inclusion theorem similar to a wellknown result of Taibleson for such spaces over ${\textbf {R}^n}$.

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## Bibliographic Information

- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**258**(1980), 155-165 - MSC: Primary 43A70; Secondary 26A33
- DOI: https://doi.org/10.1090/S0002-9947-1980-0554325-1
- MathSciNet review: 554325