Let D_Γ = R^n + iΓ be the tube domain over a proper and nonempty open convex cone Γ ⊂ R^n, and P the Bergman projection from L^2 (D_Γ) onto its subspace L^2_hol (D_Γ) of all holomorphic functions. We prove that P is bounded in the whole range 1 < p < ∞ if Γ is a polyhedral cone (i.e. the intersection of a finite number of open half- spaces). An analogous assertion is also obtained for type II Siegel domains associated to the cone Γ.
L^p-boundedness of Bergman projection associated to polyhedral cones
CIATTI, PAOLO;
2004
Abstract
Let D_Γ = R^n + iΓ be the tube domain over a proper and nonempty open convex cone Γ ⊂ R^n, and P the Bergman projection from L^2 (D_Γ) onto its subspace L^2_hol (D_Γ) of all holomorphic functions. We prove that P is bounded in the whole range 1 < p < ∞ if Γ is a polyhedral cone (i.e. the intersection of a finite number of open half- spaces). An analogous assertion is also obtained for type II Siegel domains associated to the cone Γ.
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