Timeline for Fourier Coefficients and Hölder Continuity
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 1, 2013 at 0:31 | comment | added | Matt Jacobs | Thank you for the great diagram and explanation. Is there a reason that this problem becomes easy again for $C^{\infty}$ functions? | |
| Feb 1, 2013 at 0:30 | vote | accept | Matt Jacobs | ||
| Jan 31, 2013 at 17:36 | comment | added | Terry Tao | ... and so one cannot hope for really sharp criteria based only on the magnitude of individual Fourier coefficients. (However, thanks to Littlewood-Paley theory, which has much better L^p stability properties than the Fourier transform, one can get good control in terms of Littlewood-Paley components of the function, as Bazin points out below. ) | |
| Jan 31, 2013 at 17:34 | comment | added | Terry Tao | As a general rule, the further away the integrability exponent $p$ of a physical space-based function space is from the Hilbert exponent $2$, the harder it is to control the norm via the magnitude of the Fourier coefficients (basically because analogues of the Plancherel identity, such as the Hanner inequalities or the Hausdorff-Young inequalities, become less and less efficient as one moves further away from 2). The Holder classes have exponent $\infty$ (as depicted for instance in this diagram of mine: terrytao.wordpress.com/2010/03/11/… ) ... | |
| Jan 30, 2013 at 21:10 | history | edited | Pietro Majer | CC BY-SA 3.0 |
edited body; edited title
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| Jan 30, 2013 at 20:29 | answer | added | Bazin | timeline score: 11 | |
| Jan 30, 2013 at 19:44 | answer | added | Gian Maria Dall'Ara | timeline score: 5 | |
| Jan 30, 2013 at 17:37 | answer | added | Daniel Spector | timeline score: 5 | |
| Jan 30, 2013 at 16:28 | history | asked | Matt Jacobs | CC BY-SA 3.0 |