Timeline for Operators from $L^{\infty}$ to $L^{\infty}$
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Jul 5, 2013 at 16:01 | history | edited | Bazin | CC BY-SA 3.0 |
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| Jul 5, 2013 at 16:00 | comment | added | Bazin | @Danqing You are right, I have withdrawn the middle part of my answer. The commutation of the essential supremum with a supremum may pose some problems. | |
| Jul 4, 2013 at 20:43 | comment | added | Danqing | Thank yo for you answer, but there is still one point which I don't understand and can you help me to make it clear? I agree that $$ ess\sup \int|K(\cdot,y)|dy\le ess\sup_{x}\ \sup_{\|u\|_{L^{\infty}=1}}|(Tu)(x)|, $$ but how can we get rid of the $\sup$ in the RHS since $\sup_{\|u\|_{L^{\infty}=1}}|(Tu)(x)|$ may be $\infty$ for some point $x$. | |
| Jul 4, 2013 at 20:14 | history | answered | Bazin | CC BY-SA 3.0 |