Regarding the value of an expression

Question

Let $s>0$, and let $r\in [0,1)$. Consider the value $I_s(r)=\frac{2}{1-s}((1-r+\pi)^{1-s}-(1-r)^{1-s})$. The last line of of the proof of Lemma 1.2 in this article on Hardy Spaces says that

$I_s(r)\asymp 1$ if $s<1$

and $I_s(r)\asymp (1-r)^{-(s-1)}$ if $s>1.$ Can anyone tell how?

Answer 1

Check the proof of lemma 2.15 here.