Timeline for Marcinkiewicz-Mihlin-Hormander Fourier multiplier theorem
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| S Jun 27, 2020 at 19:08 | history | suggested | Daniele Tampieri | CC BY-SA 4.0 |
Minor Math Jaxing (formula hyperlinking + other minor cares) + minor grammar improvements and formatting
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| Jun 27, 2020 at 18:42 | review | Suggested edits | |||
| S Jun 27, 2020 at 19:08 | |||||
| Jun 27, 2020 at 16:54 | comment | added | user90189 | Your second definition of $L^2_\alpha$ is right. Notice that $|\partial^j(\chi m(tx))|\le\sum_l c_lt^l|\partial^{j-l}\chi\,(\partial^l m)(tx)|\le C\sum_l|\partial^{j-l}\chi||x|^{-l}$ and the $L^2$-norm is uniformly bounded. The symbol $e^{i|\xi|^2}$ doesn't satisfy the hypotheses; furthermore, the $L^p\to L^p$ bound only holds for $p=2$; use examples $e^{i|x|^2}f$ for suitable functions $f$, say $f=1/(1+|x|^2)^\alpha$ for $\alpha<n/2$. | |
| Jun 27, 2020 at 15:34 | history | edited | Learn | CC BY-SA 4.0 |
added 167 characters in body; edited tags
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| Jun 27, 2020 at 13:40 | history | asked | Learn | CC BY-SA 4.0 |