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 Holder constant of its k-th derivative. We apply these inequalities in order to obtain pointwise estimates on the derivative of the (k + alpha)-th root of a function of class C-k whose derivative of order k is alpha-Holder 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.
Autori interni: | |
Autori: | Ghisi, Marina; Gobbino, Massimo |
Titolo: | Higher order Glaeser inequalities and optimal regularity of roots of real functions |
Anno del prodotto: | 2013 |
Digital Object Identifier (DOI): | 10.2422/2036-2145.201107_011 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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