Timeline for A domination property for the Hardy space $H^1$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Sep 19, 2020 at 14:28 | comment | added | an_ordinary_mathematician | So that, combined with the observation about the Herglotz transform above is a quite roundabout proof that the Hilbert transform is unbounded on $L^1(\mathbb{T})$ ! | |
| Sep 19, 2020 at 14:25 | history | bounty ended | an_ordinary_mathematician | ||
| Sep 19, 2020 at 14:16 | comment | added | fedja | @an_ordinary_mathematician The square root of a function with non-negative real part has non-negative real part, doesn't it? $|\Im g|\le|\Re g|$ is insufficient because it isn't preserved under weak limits. $\sqrt 2$ is there, of course, but it is just absorbed into $C$. | |
| Sep 19, 2020 at 9:12 | comment | added | an_ordinary_mathematician | Thanks a lot, this is very nice ! Doing the calculations I don't see whe $\Re g$ is positive, I get instead $| \Im g| \leq |\Re g | $ and $\sqrt{2} |\Re g| \geq f$. Probably I am missing something. | |
| Sep 19, 2020 at 8:54 | vote | accept | an_ordinary_mathematician | ||
| Sep 19, 2020 at 0:15 | history | edited | fedja | CC BY-SA 4.0 |
added 2 characters in body
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| Sep 18, 2020 at 18:54 | history | answered | fedja | CC BY-SA 4.0 |