Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces

Details Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces

2010-07-07

arxiv.org/abs/1007.1082v1

Journal of Mathematical Analysis and Applications. Vol: 377 (2011), pp. 353-361

Mathematics

Complex Variables

Scientific paper

10.1016/j.jmaa.2010.10.074

We characterize the Schatten class membership of the canonical solution operator to $\bar\partial$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in terms of $\Delta\phi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\phi})$.

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