高阶Glaeser不等式与实函数根的最优正则性
Higher order Glaeser inequalities and optimal regularity of roots of real functions
摘要：
证明了Glaeser不等式的一个高阶推广，根据该不等式，可以用函数本身及其k阶导数的Holder常数来估计函数的一阶导数.我们应用这些不等式，以获得C^{k}类函数的（k+alpha）次根的导数的逐点估计，其k阶导数是alpha-Holder连续的。由于这样的估计，我们证明了根不仅是绝对连续的，但它的衍生物有一个更高的求和指数。一些例子表明，我们的结果是最优的。
英文摘要：
We prove a higher order generalization of 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
