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$L^p$ regularity of the Bergman projection on the symmetrized polydisc
We study the 
$L^p$ regularity of the Bergman projection P over the symmetrized polydisc in 
$\mathbb C^n$. We give a decomposition of the Bergman projection on the polydisc and obtain an operator equivalent to the Bergman projection over antisymmetric function spaces. Using it, we obtain the 
$L^p$ irregularity of P for 
$p=\frac {2n}{n-1}$ which also implies that P is 
$L^p$ bounded if and only if 
$p\in (\frac {2n}{n+1},\frac {2n}{n-1})$.
