论文标题
Szegő和Bergman对平面域的预测结果
Some Results for the Szegő and Bergman Projections on Planar Domains
论文作者
论文摘要
本说明的目的是证明使用保形映射对某些类别的平面域上的谐波分析风味的一些有界性/紧凑性结果。特别是，我们证明了预测的加权估计值，提供了定量的$ l^p $估计值，以及具有尖锐$ p $范围的域上的此类估计值的特定示例，并表明伯格曼和szegő预测的``差异''在端点上是紧凑的，在端点$ p = 1，\ infty $ p = 1，\ for Affacty splosplospoolss的域。我们还提出了一些自然而然的问题，这些问题自然而然地引起了我们的调查。
The purpose of this note is to prove some boundedness/compactness results of a harmonic analysis flavor for the Bergman and Szegő projections on certain classes of planar domains using conformal mappings. In particular, we prove weighted estimates for the projections, provide quantitative $L^p$ estimates and a specific example of such estimates on a domain with a sharp $p$ range, and show that the ``difference'' of the Bergman and Szegő projections is compact at the endpoints $p = 1, \infty$ for domains with sufficient smoothness. We also pose some open questions that naturally arise from our investigation.
