The Bergman projection on Hartogs domains in 𝐶²

Boas, Harold P.; Straube, Emil J.

doi:10.1090/S0002-9947-1992-1062188-1

The Bergman projection on Hartogs domains in $\textbf {C}^ 2$
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Trans. Amer. Math. Soc. 331 (1992), 529-540 Request permission

Abstract:

Estimates in ${L^2}$ Sobolev norms are proved for the Bergman projection in certain smooth bounded Hartogs domains in ${{\mathbf {C}}^2}$. In particular, (1) if the domain is pseudoconvex and "nonwormlike" (the normal vector does not wind on a critical set in the boundary), then the Bergman projection is regular; and (2) Barrett’s counterexample domains with irregular Bergman projection nevertheless admit a priori estimates.

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