Timeline for Decoupling Implies Local Decoupling
Current License: CC BY-SA 3.0
7 events
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| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jun 19, 2016 at 4:59 | comment | added | Terry Tao | Section 4 of Bourgain and Demeter's study guide arxiv.org/pdf/1604.06032.pdf has some tools to replace one weight with another, more or less for this sort of reason. | |
| Jun 19, 2016 at 1:58 | comment | added | Matt Rosenzweig | @TerryTao Thank you; your comment is very helpful. When I follow your suggest, I end up with expressions like $$(\sum_{\theta\in\mathcal{P}_{\delta}}\|(\widehat{g_{\theta}d\sigma}\ast K_{\theta})\|_{L^{p}(w_{B_{\delta^{-1}}})}^{2})^{1/2}$$ on the RHS, where $K_{\theta}$ is the convolution resulting from the partition of unity applied to $g$ (see (3) in my edited answer). In trying to remove the $K_{\theta}$, I end up with the desired RHS with another weight $\tilde{w}_{B_{\delta^{-1}}}$, which is not necessarily Fourier supported in $B(0,\delta)$. | |
| Jun 19, 2016 at 1:54 | history | edited | Matt Rosenzweig | CC BY-SA 3.0 |
added 3053 characters in body
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| Jun 18, 2016 at 17:02 | comment | added | Terry Tao | You can use the sparsification trick. By partitioning the space of caps into $O(1)$ collections of $\delta^{1/2}$-separated caps and using the triangle inequality (and maybe a smooth partition of unity), one can assume without loss of generality that $g$ is supported on one of these sparsified collections, at which point one can use smooth cutoffs instead of rough ones. | |
| Jun 18, 2016 at 14:21 | history | edited | Matt Rosenzweig | CC BY-SA 3.0 |
Added link to related question.
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| Jun 18, 2016 at 14:08 | history | asked | Matt Rosenzweig | CC BY-SA 3.0 |