One-Parameter Families of Operators in $\mathbb{C}$

Details One-Parameter Families of Operators in $\mathbb{C}$ One-Parameter Families of Operators in $\mathbb{C}$

2005-08-29

arxiv.org/abs/math/0508569v2

J. Geom. Anal., 16(2):353-374, 2006

Mathematics

Complex Variables

v2: 18 pages. AMS-LaTeX. Updated references, numerous errors/typos fixed

Scientific paper

We develop classes of one-parameter families (OPF) of operators on $C^\infty_c(\mathbb{C})$ which characterize the behavior of operators associated to the $\bar\partial$-problem in $L^2(\mathbb{C},e^{-2p})$ where $p$ is a subharmonic, nonharmonic polynomial. We prove that an order 0 OPF operator extends to a bounded operator from $L^q(\mathbb{C})$ to itself, $1

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