Resumen de Higher order Glaeser inequalities and optimal regularity of roots of real functions
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 H¨older 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 Ck 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
