Fractional differentiation and Lipschitz spaces on local fields

Author:
C. W. Onneweer

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

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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 for functions in , . 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 -differentiable functions of order when . 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 .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1980-0554325-1

Keywords:
Local fields,
fractional derivatives,
Bessel potentials,
generalized Lipschitz spaces

Article copyright:
© Copyright 1980
American Mathematical Society