Compactness of the Canonical Solution Operator of on Bounded Pseudoconvex Domains

Knirsch, Wolfgang

doi:10.1002/1522-2616(200211)245:1<94::aid-mana94>3.0.co;2-h

Math. Nachr.

2002

DOI: 10.1002/1522-2616(200211)245:1<94::aid-mana94>3.0.co;2-h

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Compactness of the Canonical Solution Operator of on Bounded Pseudoconvex Domains

Wolfgang Knirsch

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Cited by 2 publications

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The canonical solution operator of $ {\bar \partial } $ on weighted spaces with holomorphic coefficients

Knirsch

2004

Mathematische Nachrichten

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Key wordsOn weighted spaces with strictly plurisubharmonic weightfunctions the canonical solution operator of ∂ and the ∂-Neumann operator are bounded. In this paper we find a class of strictly plurisubharmonic weightfunctions with certain growth conditions, so that they are Hilbert-Schmidt operators between weighted spaces with different weightfunctions, if they are restricted to forms with holomorphic coefficients.

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The canonical solution operator of $ {\bar \partial } $ on weighted spaces with holomorphic coefficients

Knirsch

2004

Mathematische Nachrichten

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Continuity and Schatten–von Neumann p-class membership of Hankel operators with anti-holomorphic symbols on (generalized) Fock spaces

Knirsch

Schneider

2006

Journal of Mathematical Analysis and Applications

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In this paper we investigate Hankel operators H f :where A 2 m are general Fock spaces. We will show that H f is not continuous if the corresponding symbol is not a polynomial f = N k=0 b k z k . For polynomial symbols we will give necessary and sufficient conditions for continuity and compactness in terms of N and m. For monomials z k we will give a complete characterization of the Schatten-von Neumann p-class membership for p > 0. Namely in case 2k < m the Hankel operators H z k are in the Schattenvon Neumann p-class iff p > 2m/(m−2k); and in case 2k m they are not in the Schatten-von Neumann p-class.

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Compactness of the Canonical Solution Operator of on Bounded Pseudoconvex Domains

Cited by 2 publications

References 4 publications

The canonical solution operator of $ {\bar \partial } $ on weighted spaces with holomorphic coefficients

The canonical solution operator of $ {\bar \partial } $ on weighted spaces with holomorphic coefficients

Continuity and Schatten–von Neumann p-class membership of Hankel operators with anti-holomorphic symbols on (generalized) Fock spaces

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