Doing my homework on functional analysis I faced with the following problem.
Let $\displaystyle (Uf) (s)=\int\limits_{-1}^{1}\frac{f(t)}{|s-t|^{5/6}}dt$. Using Young inequality it can be shown that $U$ is bounded operator from $L^3(-1,1)$ to $L^r(-1,1)$ with $r<6$ and it is compact. If $r>6$ then it is easy to see (by considering functions of the form $f(t)=1/t^\beta$) that $U$ is not bounded from $L^3(-1,1)$ to $L^r(-1,1)$. But I don't know how to investigate the case when $r=6$.
Is $U$ bounded or even compact from $L^3(-1,1)$ to $L^6(-1,1)$?