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arXiv · 2210.10640

The Commutator of the Bergman Projection on Strongly Pseudoconvex Domains with Minimal Smoothness

Bingyang Hu·Zhenghui Huo·Loredana Lanzani·Kevin Palencia·Nathan A. Wagner
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Abstract

Consider a bounded, strongly pseudoconvex domain $D\subset \mathbb C^n$ with minimal smoothness (namely, the class $C^2$) and let $b$ be a locally integrable function on $D$. We characterize boundedness (resp., compactness) in $L^p(D), p > 1$, of the commutator $[b, P]$ of the Bergman projection $P$ in terms of an appropriate bounded (resp. vanishing) mean oscillation requirement on $b$. We also establish the equivalence of such notion of BMO (resp., VMO) with other BMO and VMO spaces given in the literature. Our proofs use a dyadic analog of the Berezin transform and holomorphic integral representations going back (for smooth domains) to N. Kerzman & E. M. Stein, and E. Ligocka.

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Bingyang Hu, Zhenghui Huo, Loredana Lanzani, Kevin Palencia, Nathan A. Wagner. 2022-10-19. The Commutator of the Bergman Projection on Strongly Pseudoconvex Domains with Minimal Smoothness. https://arxiv.org/abs/2210.10640

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