L^p regularity of the Bergman projection on the symmetrized polydisc

We study the Lp regularity of the Bergman projection P over the symmetrized polydisc in ℂn. 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 Lp irregularity of P=2n/n-1 which also implies that P is Lp bounded if and only if p ∈(2n/n+1, 2n/n-1).

Duke Scholars

Author Zhenghui Huo DKU Faculty