One-Parameter Families of Operators in $\mathbb{C}$
| dc.creator | Raich, Andrew | |
| dc.date | 2005-08-29 | |
| dc.date | 2006-06-30 | |
| dc.date.accessioned | 2026-07-07T06:42:51Z | |
| dc.date.available | 2026-07-07T06:42:51Z | |
| dc.description | 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, $1<q<\infty$, with a bound that depends on $q$ and the degree of $p$ but not on the parameter $τ$ or the coefficients of $p$. Last, we show that there is a one-to-one correspondence given by the partial Fourier transform in $τ$ between OPF operators of order $m\leq 2$ and nonisotropic smoothing (NIS) operators of order $m\leq 2$ on polynomial models in $\mathbb{C}^2$. | |
| dc.description | v2: 18 pages. AMS-LaTeX. Updated references, numerous errors/typos fixed | |
| dc.identifier | https://arxiv.org/abs/math/0508569 | |
| dc.identifier | http://arxiv.org/abs/math/0508569 | |
| dc.identifier | J. Geom. Anal., 16(2):353-374, 2006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102199 | |
| dc.subject | Complex Variables | |
| dc.subject | 32W50 (Primary), 32W30, 32T25 (Secondary) | |
| dc.title | One-Parameter Families of Operators in $\mathbb{C}$ | |
| dc.type | text |