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Abstract We study the$$L^p$$regularity of the Bergman projectionPover 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 ofPfor$$p=\frac {2n}{n-1}$$which also implies thatPis$$L^p$$bounded if and only if$$p\in (\frac {2n}{n+1},\frac {2n}{n-1})$$.
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Projections onto L^p Bergman spaces of Reinhardt domains
For $$1<\infty$$, we emulate the Bergman projection on Reinhardt domains by using a Banach-space basis of $L^p$-Bergman space. The construction gives an integral kernel generalizing the ($L^2$) Bergman kernel. The operator defined by the kernel is shown to be an absolutely bounded projection on the $L^p$-Bergman space on a class of domains where the $L^p$-boundedness of the Bergman projection fails for certain $$p \neq 2$$. As an application, we identify the duals of these $L^p$-Bergman spaces with weighted Bergman spaces.
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- Award ID(s):
- 2153907
- PAR ID:
- 10527008
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Advances in Mathematics
- Volume:
- 451
- Issue:
- C
- ISSN:
- 0001-8708
- Page Range / eLocation ID:
- 109790
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.aim.2024.109790
