Higher order Glaeser inequalities and optimal regularity of roots of real functions
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 4, pp. 1001-1021.

We prove a higher order generalization of the Glaeser inequality, according to which one can estimate the first derivative of a function in terms of the function itself and the Hölder constant of its k-th derivative.

We apply these inequalities in order to obtain pointwise estimates on the derivative of the (k+α)-th root of a function of class C k whose derivative of order k is α-Hölder continuous. Thanks to such estimates, we prove that the root is not just absolutely continuous, but its derivative has a higher summability exponent.

Some examples show that our results are optimal.

Publié le :
Classification : 26A46, 26B30, 26A27
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     title = {Higher order {Glaeser} inequalities and optimal regularity of roots of real functions},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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Ghisi, Marina; Gobbino, Massimo. Higher order Glaeser inequalities and optimal regularity of roots of real functions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 4, pp. 1001-1021. http://archive.numdam.org/item/ASNSP_2013_5_12_4_1001_0/

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