SCHWEITZER 1992 Problem 6

Let $E \subset [0,1]$ be a Lebesgue measurable set having Lebesgue measure $| E |<\frac{1}{2}$ . Let $$h (s) = \int _ {\overline {E}} \frac{dt}{{(s-t)}^2}$$ where $\overline {E} = [0,1] \backslash E$ . Prove that there is one $t \in \overline {E}$ for which $$\int_E \frac {ds} {h (s) {(s-t)} ^ 2} \leq c {| E |} ^ 2$$ with some absolute constant c .