Weighted Bergman projections on the Hartogs triangle
Copyright policy )Weighted Bergman projections on the Hartogs triangle
We prove the $L^p$ regularity of the weighted Bergman projection on the Hartogs triangle, where the weights are powers of the distance to the singularity at the boundary. The restricted range of $p$ is proved to be sharp. By using a two-weight inequality on the upper half plane with Muckenhoupt weights, we can consider a slightly wider class of weights.
The article has been revised. There are 23 pages in total
- The Ohio State University United States
\(L^p\) regularity, Mathematics - Complex Variables, Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube), Hartogs triangle, Mathematics - Classical Analysis and ODEs, Integral representations; canonical kernels (Szegő, Bergman, etc.), Classical Analysis and ODEs (math.CA), FOS: Mathematics, Bergman projection, Complex Variables (math.CV)
\(L^p\) regularity, Mathematics - Complex Variables, Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube), Hartogs triangle, Mathematics - Classical Analysis and ODEs, Integral representations; canonical kernels (Szegő, Bergman, etc.), Classical Analysis and ODEs (math.CA), FOS: Mathematics, Bergman projection, Complex Variables (math.CV)
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