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

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