Timeline for Some detail in Fefferman's thesis
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 19, 2016 at 3:39 | comment | added | user134927 | Is $x-y'$ really varies within a constant factor? $x \nsim I_j$ means x either outside the collection of cube or belongs to one of the cube which is not $I_j$ and not touch $I_j$ . $x$ can be far away from $y'$ or near $y'$. | |
| Oct 18, 2016 at 15:21 | comment | added | Fan Zheng | Not really. It is equivalent to prove $J^{n\theta/2}(x-y')$ is comparable when $y'=y+d_j^{1/(1-\theta)}$ ranges over the double of $I_j$. Morally this follows from the behavior of the Bessel potential near 0 and infinity. Near 0 it diverges by a power law, so if its argument varies within a constant factor then its values are comparable. Near infinity it decays by an exponential law, so if its argument varies within a constant distance then its values are comparable. All these are satisfied in your situation, but I have to look up the asymptotics more carefully before i can write up an answer. | |
| Oct 18, 2016 at 4:51 | comment | added | user134927 | It is equivalent to prove $J^{\frac{n\theta}{2}}(x-y-d_j^{\frac{1}{1-\theta}}z)$ is bounded which I have no idea. | |
| Oct 17, 2016 at 18:11 | comment | added | Fan Zheng | Are you able to show $\sup_{y\in I_j, |z|<1} J^{n\theta/2} (x-y-d_j^{1/(1-\theta)}z)<C\inf_{y\in I_j, |z|<1} J^{n\theta/2} (x-y-d_j^{1/(1-\theta)}z)$? | |
| Oct 17, 2016 at 3:02 | review | First posts | |||
| Oct 17, 2016 at 3:24 | |||||
| Oct 17, 2016 at 2:58 | history | asked | user134927 | CC BY-SA 3.0 |