The Bergman projection in $L^p$ for domains with minimal smoothness

By Loredana Lanzani, E. Stein. 2012

66 citations recorded by the source corpus.

Let $D\subset\mathbb C^n$ be a bounded, strongly Levi-pseudoconvex domain with minimally smooth boundary. We prove $L^p(D)$-regularity for the Bergman projection $B$, and for the operator $|B|$ whose kernel is the absolute value of the Bergman kernel with $p$ in the range $(1,+\infty)$. As an application, we show that the space of holomorphic functions in a neighborhood of $\bar{D}$ is dense in $\vartheta L^p (D)$.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/000a6d1199008cfc498f30f864a21b17011582ce

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In Applied Mathematics

1. L. Edholm
2. Jeffery D. McNeal
3. E. Straube
4. Siqi Fu

In Geometry and Topology

1. L. Edholm
2. Jeffery D. McNeal
3. E. Straube
4. Siqi Fu

Citations in the corpus

• Bergman Subspaces and Subkernels: Degenerate $$L^p$$Lp Mapping and Zeroes (2016, background): “em 1.2 in [26] is lacking, but would be very interesting. For many classes of pseudoconvex domains with smooth boundary it is known that the Bergman projection maps Lp boundedly for all p∈ (1,∞), see [23, 19, 20, 21, 22, 18] and their references for the principal results. But recently, restricted Lp”