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Published in:
2016 | OriginalPaper | Chapter
Hölder and locally Hölder continuous functions. The linear spaces
Author : Renato Fiorenza
Published in: Hölder and locally Hölder Continuous Functions, and Open Sets of Class C^k, C^{k,lambda}
Publisher: Springer International Publishing
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In Section 1.1, after the introduction of the classic notion of Hölder continuous function and the related terminology, we will highlight some properties of these functions (uniform continuity, boundedness, extendability), adding some observations (e.g., the non-existence, in general, of the maximum Hölder exponent) and the comparison with the notions of uniform continuity and absolute continuity; when necessary, we will give counterexamples. Among other things, we will prove a first Lipschitz continuity criterion for functions having continuous and bounded first derivatives.