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Characterization of Pointwise Hölder Regularity

✍ Scribed by Patrik Andersson

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
251 KB
Volume
4
Category
Article
ISSN
1063-5203

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✦ Synopsis

We study different characterizations of the pointwise Ho ¨lder spaces C s (x 0 ), including rate of approximation by smooth functions and iterated differences. As an application of our results we study the class of functions that are Ho ¨lder exponents and prove that the Ho ¨lder exponent of a continuous function is the limit inferior of a sequence of continuous functions, thereby improving a theorem of S. Jaffard. ᭧ 1997 Academic Press but the converse does not hold. To obtain a converse we have to assume that, in addition to (1.1), f satisfies a global regularity condition, and we can only conclude that Éf ( x) 0 P(x 0 x 0 )É £ CÉx 0 0 x 0 É s log(1/Éx 0 x 0 É). See [4] for proofs, counterexamples, and more details.

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