Sharp estimates for the operator \(\overline{\partial}_M\) on a \(q\)-concave CR-manifold
type: Item
instance of: scholarly article
title: Sharp estimates for the operator \(\overline{\partial}_M\) on a \(q\)-concave CR-manifold
zbMATH Open document ID: 0909.32005
DOI: 10.1007/BF02921601
author: Peter L. Polyakov
published in: The Journal of Geometric Analysis
publication date: 1998-08-10T00:00:00Z
review text: Let \(M\) be a regular \(q\)-concave CR-manifold (\(q \geq 2\)) of class \(C^{4}\) and let \(M\) be a relatively compact open subset of \(M\). For any \(r=1, \dots, q-1 \), the author proves the existence of a compact operator \(H_{r}\) and of a linear operator \(R_{r}\) with sharp estimates acting on the space of \((0,r)\)-differential forms such that for such a form \(f\) the following holds for each point \(z\) of \(M\): \( f(z)= \overline{\partial }_{M} R_{r}(f) (z) + R_{r+1} (\overline{\partial }_{M} f) (z) + H_{r}(f) (z) \).
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 32V99
Mathematics Subject Classification ID: 32F10
Mathematics Subject Classification ID: 32A25
zbMATH DE Number: 1160135
zbMATH Keywords: \( \overline{\partial } \)-operator
zbMATH Keywords: \(q\)-concave-CR-manifold
zbMATH Keywords: differential forms
zbMATH Keywords: integral representations
reviewed by: Eugen Pascu
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02921601
OpenAlex ID: W2326668818
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description: scientific article; zbMATH DE number 1160135