Canonical homotopy operators for the $\overline{\partial }$ complex in strictly pseudoconvex domains

Mats Andersson; Jörgen Boo; Joaquim Ortega-Cerdà

Displaying similar documents to “Canonical homotopy operators for the $\bar{\partial}$ complex in strictly pseudoconvex domains”

On canonical homotopy operators for ∂ in Fock type spaces in C.

Jörgen Boo (2001)

Publicacions Matemàtiques

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We show that a certain solution operator for ∂ in a space of forms square integrable against e^-|z|² is canonical, i.e., that it gives the minimal solution when applied to a ∂-closed form, and gives zero when applied to a form orthogonal to Ker ∂. As an application, we construct a canonical homotopy operator for i∂∂.

Remarks on the Bergman kernel function of a worm domain

Ewa Ligocka (1998)

Studia Mathematica

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We use a recent result of M. Christ to show that the Bergman kernel function of a worm domain cannot be $C^{\infty}$ -smoothly extended to the boundary.

On the Forelli-Rudin construction and weighted Bergman projections

Ewa Ligocka (1989)

Studia Mathematica

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The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman

Bo Berndtsson (1996)

Annales de l'institut Fourier

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We give a short proof of the extension theorem of Ohsawa-Takegoshi. The same method also gives a generalization of the $\overline{\partial}$ -theorem of Donnelly and Fefferman for the case of $(n, 1)$ -forms.

The Hölder continuity of the Bergman projection and proper holomorphic mappings

Ewa Ligocka (1984)

Studia Mathematica

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Formulas for approximate solutions of the ∂∂`-equation in a strictly pseudoconvex domain.

Mats Andersson, Hasse Carlsson (1995)

Revista Matemática Iberoamericana

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Let D be a bounded strictly pseudoconvex domain in C. We construct approximative solution formulas for the equation i∂∂`u = θ, θ being an exact (1,1)-form in D. We show that our formulas give simple proofs of known estimates and indicate further applications.

On the orthogonal projections onto spaces of pluriharmonic functions and duality

Ewa Ligocka (1986)

Studia Mathematica

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Values in the interior of the L-minimal solutions of the ∂∂-equation in the unit ball of C.

Mats Andersson (1988)

Publicacions Matemàtiques

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We derive formulas for the values in the interior of the L-minimal solutions of the ∂∂-equation in the unit ball of C. These formulas generalize previously known formulas for the boundary values of the same solutions. We estimate the solution and obtain a (known) result concerning weighted Nevanlinna classes.

On boundary behaviour of Bergman kernel function for plane domains and their Cartesian products

Ewa Ligocka (1983)

Banach Center Publications

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Displaying similar documents to “Canonical homotopy operators for the ∂ ¯ complex in strictly pseudoconvex domains”

Displaying similar documents to “Canonical homotopy operators for the $\bar{\partial}$ complex in strictly pseudoconvex domains”