Bergman subspaces and subkernels: Degenerate $L^p$ mapping and zeroes

Abstract

Regularity and irregularity of the Bergman projection on $L^p$ spaces is established on a natural family of bounded, pseudoconvex domains. The family is parameterized by a real variable $\gamma$. A surprising consequence of the analysis is that, whenever $\gamma$ is irrational, the Bergman projection is bounded only for $p=2$.

21 pages, 2 figures

References in corpus (3)

• The Bergman projection on fat Hartogs triangles: L^p boundedness
• Bergman theory of certain generalized Hartogs triangles
• The Bergman kernel and projection on non-smooth worm domains

Cited by in corpus (18)

• $L^p$-regularity of the Bergman projection on quotient domains
• Duality and approximation of Bergman spaces
• Bergman Kernels of Elementary Reinhardt Domains
• Weak-type estimates for the Bergman projection on the polydisc and the Hartogs triangle
• Sobolev mapping of some holomorphic projections
• Weighted estimates for the Bergman projection on the Hartogs triangle
• Weighted Bergman Projections on the Hartogs Triangle: Exponential Decay
• Projections onto $L^p$-Bergman spaces of Reinhardt Domains
• Hardy Spaces for a Class of Singular Domains
• $L^p$ regularity of the Bergman projection on the symmetrized polydisc
• Nonabelian ramified coverings and $L^p$-boundedness of Bergman projections in ${\mathbb{C}}^2$
• Special Toeplitz operators on a class of bounded Hartogs domains
• $L^p$ regularity of the Bergman Projection on domains covered by the polydisk
• Smoothing Properties of the Friedrichs Operator on $L^p$ spaces
• Norm convergence of partial sums of $H^1$ functions
• $L^p$ estimates for the Bergman projection on some Reinhardt domains
• A solution operator for $\bar{\partial }$ on the Hartogs triangle and $L^p$ estimates
• A remark on Carleson measures of domains in ${\mathbb{C}}^n$