# on Lipschitz function

let $$A$$ an N-function such that

$$\int^{+\infty}_1\frac{A^{-1}(\tau)}{\tau^{1+\frac{1}{n}}}d\tau=+\infty$$

$$\int^{1}_0\frac{A^{-1}(\tau)}{\tau^{\frac{n+1}{n}}}d\tau < +\infty$$

we define $$A^{-1}_{\ast}(t)=\int^t_0\frac{A^{-1}(\tau)}{\tau^{\frac{n+1}{n}}} d\tau$$ how we show that $$\sigma(t)=(A_{\ast}(t))^{\frac{n-1}{n}}$$ is Lipschitz on $$\mathbb{R}$$?