Let $Y_{k,j}:{\mathbb S}^{n-1}\to {\mathbb R}$ be spherical harmonics on $n-1$ -dimensional sphere.
We know that $\|Y_{k,j}\|_{L_2({\mathbb S}^{n-1})}^2 = \int_{{\mathbb S}^{n-1}}Y^2_{k,j}(x)d\sigma(x)=1$. What can be said about $L_1$-norm, i.e. how $$ \|Y_{k,j}\|_{L_1({\mathbb S}^{n-1})} $$ behaves as a function of $k$?