Timeline for Is anything known about $w^*(x)=\sup_y w(x+y)/w(y)$ for measurable functions w on $R^n$
Current License: CC BY-SA 2.5
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| Jun 30, 2010 at 19:57 | comment | added | Willie Wong | Oh hey, looks like your answer is more or less in a similar vein to mine. Cool. | |
| Jun 30, 2010 at 19:34 | comment | added | Helge | I would guess that a converse also holds: Assume $w$ has subexponential growth and is 'monotone' then this property holds. Idea of proof: 'subexponential growth' => I can restrict to a compact set. On compact set $w*(x)$ and $w(x)$ are continuous, so one has $w*(x) \leq C w(x)$ for some $C$... But I didn't try to make this rigorous. | |
| Jun 30, 2010 at 19:29 | history | answered | Helge | CC BY-SA 2.5 |