In this paper we prove that on a CR manifold of hypersurface type that satisfies the weak condition, the complex Green operator is exactly (globally) regular if and only if the Szegö projections and a third orthogonal projection are exactly (globally) regular. The projection is closely related to the Szegö projection and actually coincides with it if the space of harmonic -forms is trivial. This result extends the important and by now classical result by H. Boas and E. Straube on the equivalence of the regularity of the -Neumann operator and the Bergman projections on a smoothly bounded pseudoconvex domain. We also prove an extension of this result to the case of bounded smooth domains satisfying the weak condition on a Stein manifold.
Regularity equivalence of the Szegö projection and the complex Green operator / P.S. Harrington, M.M. Peloso, A.S. Raich. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 1088-6826. - 143:1(2015 Jan), pp. 353-367. [10.1090/S0002-9939-2014-12393-8]
Regularity equivalence of the Szegö projection and the complex Green operator
M.M. Peloso;
2015
Abstract
In this paper we prove that on a CR manifold of hypersurface type that satisfies the weak condition, the complex Green operator is exactly (globally) regular if and only if the Szegö projections and a third orthogonal projection are exactly (globally) regular. The projection is closely related to the Szegö projection and actually coincides with it if the space of harmonic -forms is trivial. This result extends the important and by now classical result by H. Boas and E. Straube on the equivalence of the regularity of the -Neumann operator and the Bergman projections on a smoothly bounded pseudoconvex domain. We also prove an extension of this result to the case of bounded smooth domains satisfying the weak condition on a Stein manifold.File | Dimensione | Formato | |
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