# Sobolev Spaces and Derivative

I need help on the problem 8.9 at page 238 of the book "Functional Analysis, Sobolev Spaces and Partial Differential Equations" by Haim Brezis.

Set $I=(0,1)$.
Let $u \in W^{2,p}(I)$ with $1<p<\infty$.
Assume that $u(0)=u'(0)=0$.
Show that $$\frac{u(x)}{x^2}\in L^p(I)\quad\text{and}\quad \frac{u'(x)}{x}\in L^p(I),$$ with $$\left|\left|\frac{u(x)}{x^2}\right|\right|_{L^p(I)}+ \left|\left|\frac{u'(x)}{x}\right|\right|_{L^p(I)} \leq C_p\left|\left|u''\right|\right|_{L^p(I)}.$$

Thank you in advance for any help.