An explicit ̄∂-integration formula for weighted homogeneous varieties

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Aug 2009Publisher:Michigan Mathematical JournalJournal:Michigan Mathematical Journal, volume 58 (issn: 0026-2285,

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Authors: Ruppenthal, Jean; Zeron, E. S.;

doi: 10.1307/mmj/1250169071

An explicit ̄∂-integration formula for weighted homogeneous varieties

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Abstract

Let be a weighted homogeneous (singular) subvariety of C n . The main objective of this paper is to present an explicit integral formula for solving the @-equation = @g on the regular part of , where is a @-closed (0; 1)-form with compact support. This formula will then be used to give Holder estimates for the solution in case is homogeneous with an isolated singularity and is bounded. A slight modication of the formula also gives an L 2 -bounded solution operator in case is pure dimensional and homogeneous (but with arbitrary singular locus).

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32W05, 35N15, 32F20

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An explicit ̄∂-integration formula for weighted homogeneous varieties

An explicit ̄∂-integration formula for weighted homogeneous varieties

10 Research products, page 1 of 1

Sobolev and Hölder estimates for $\bar{\partial}$ on bounded convex domains in $\mathbb{C}^{2}$

Subelliptic estimates for the \(\overline\partial\)-Neumann operator on piecewise smooth strictly pseudoconvex domains

An explicit d-bar-integration formula for weighted homogeneous varieties II: forms of higher degree

Equation de Lewy—Résolubilité globale de l’équation $\partial_b u = f$ sur la frontière de domaines faiblement pseudo-convexes de $\mathbf{C}^2 (\mathrm{OU} \mathbf{C}^n)$

Subelliptic estimates and failure of semicontinuity for orders of contact

Nonexistence of homotopy formula for (0,1) forms on hypersurfaces in \({\mathbb{C}}^ 3\)

Holder estimates for the $\bar\partial$-equation on surfaces with simple singularities

The range of the tangential Cauchy-Riemann operator

Local analyticity for the $\overline{\partial}$ -Neumann problem and $\square_b$ —some model domains without maximal estimates

Kernels for the local solvability of the tangential Cauchy-Riemann equations