1 results
$L^p$ regularity of the Bergman projection on the symmetrized polydisc
- Part of
-
- Journal:
- Canadian Journal of Mathematics , First View
- Published online by Cambridge University Press:
- 22 October 2024, pp. 1-26
-
- Article
-
- You have access
- HTML
- Export citation
-
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 
$p\in (\frac {2n}{n+1},\frac {2n}{n-1})$.
