<i>L</i><sup><i>p</i></sup> boundedness for the Bergman projections over <i>n</i>-dimensional generalized Hartogs triangles
Shuo Zhang
Abstract
The n-dimensional generalized Hartogs triangles are domains defined by Hpn:={(z1,…,zn)∈Cn:|z1|p1<⋯<|zn|pn<1} with p:=(p1,…,pn)∈(Z+)n and n≥2. In this paper, we first obtain an estimate for the Bergman kernel of Hpn and then use it to establish the Lp boundedness of the associated Bergman projections. Our result generalizes the Lp boundedness result for two-dimensional generalized Hartogs triangles obtained by L.D. Edholm and J.D. McNeal in [Bergman subspaces and subkernels: degenerate Lp mapping and zeroes. J Geom Anal. 2017;27:2658–2683] to n-dimensional settings.
Topics & Concepts
MathematicsBergman kernelLinear subspaceCombinatoricsBergman spaceKernel (algebra)Mathematical analysisPure mathematicsBounded functionHolomorphic and Operator TheoryAnalytic and geometric function theoryGeometry and complex manifolds