A note on Carleson sets and Carleson windows

Let $\mathbb{D}$ be the open unit disk in the complex plane. In this note, for the Carleson set $S(b,h)$ and the Carleson window $W(b,h)$ which are particular subsets of $\mathbb{D}$, we find conditions on $h$ under which we have $W(b,h\mathrm{/}c)\subset S(b,h)\subset W(b,ch)$ for some $c>1$.