论文标题
伯格曼投影的换向率，在强烈的伪内维克斯域上具有最小的平滑度
The Commutator of the Bergman Projection on Strongly Pseudoconvex Domains with Minimal Smoothness
论文作者
论文摘要
考虑一个有界的，强烈的pseudoconvex域$ d \ subset \ mathbb c^n $，具有最小的平滑度（即$ c^2 $），让$ b $是$ d $上的本地集成函数。我们在$ l^p（d），p> 1 $中表征了有界性（分别，紧凑型），伯格曼预测$ [b，p] $的伯格曼预测$ p $在适当的有限（分别消失）的$ b $上。我们还建立了这种BMO（分别，VMO）与文献中给出的其他BMO和VMO空间的等效性。我们的证明使用了Berezin Transform的二元类似物，而Holomorthic积分表示（用于平滑域）到N. Kerzman＆E。M. Stein和E. Ligocka。
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.
