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Timeline for Question about an estimate in Hörmander's proof of Cartan's Theorem B

Current License: CC BY-SA 3.0

13 events
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S Jun 26, 2013 at 19:32 history suggested Fred Daniel Kline CC BY-SA 3.0
put braces around subscripts
Jun 26, 2013 at 19:19 review Suggested edits
S Jun 26, 2013 at 19:32
Jan 13, 2013 at 11:47 answer added user80744 timeline score: 4
Jun 12, 2012 at 6:07 history edited Michael Albanese CC BY-SA 3.0
added 2 characters in body; deleted 2 characters in body
Jun 8, 2012 at 0:56 history edited Michael Albanese CC BY-SA 3.0
added 1 characters in body
Jun 7, 2012 at 18:04 comment added Mike Hall Shouldn't it just be like if you were proving Cauchy-Schwarz? Choose $|u(z)|=1$ so that the (pointwise) inner product with $(T^*(\eta_{\nu}f) - \eta_{\nu}T^*f)(z)e^{-\varphi_1(z)}$ is equal to $|(T^*(\eta_{\nu}f) - \eta_{\nu}T^*f)(z)|e^{-\varphi_1(z)}$ and then extend to a tiny bump function.
Jun 7, 2012 at 15:33 history edited Michael Albanese CC BY-SA 3.0
added 20 characters in body
Jun 7, 2012 at 15:31 comment added Michael Albanese You are correct, such $u$ are in $D_T$, but I haven't been able to explicitly determine what the 'appropriately chosen' coefficients should be. The idea is that if there was a point $z \in \Omega$ such that $(|T^*(\eta_{\nu}f) - \eta_{\nu}T^*f|^2e^{\varphi_1})(z) > (|f|^2e^{-\varphi_2})(z)$, then by taking a sequence of smooth $u$ with shrinking supports containing $z$, then the global inequality $|(T^*(\eta_{\nu}f) - \eta_{\nu}T^*f, u)_{\varphi_1}| \leq \int |f|e^{-\varphi_2/2}|u|e^{-\varphi_1/2}d\lambda$ would be violated for some particular $u$.
Jun 6, 2012 at 5:57 history edited Michael Albanese CC BY-SA 3.0
Changed the restriction on $|\bar{\partial}\eta_{\nu}|$ (initially had one from the Stein manifold case).
Jun 5, 2012 at 9:13 comment added Mike Hall I'm sure I haven't quite processed everything but it seems to follow formally, by taking $u$ with appropriately chosen $C_0^\infty$ coefficients with tiny support around a given point, right? And such $u$ lie in $D_T$, if I'm not mistaken.
Jun 5, 2012 at 7:50 history edited Michael Albanese
edited tags
Jun 5, 2012 at 3:33 history edited Michael Albanese
Added Complex Geometry, Complex Manifolds and Stein Manifolds tags.
Jun 5, 2012 at 2:38 history asked Michael Albanese CC BY-SA 3.0