Timeline for An inequality about quasi-linear function

8 events

when toggle format	what		by	license	comment
Dec 17, 2021 at 11:51	history	edited	Mr.xue	CC BY-SA 4.0	update
Dec 12, 2021 at 1:53	history	edited	Mr.xue	CC BY-SA 4.0	Add some content
Dec 12, 2021 at 1:22	comment	added	Mr.xue		@username I think that I first need to prove the inequality, then using standard Osgood lemma to prove Lemma 1.2. Is it right?
Dec 11, 2021 at 19:13	comment	added	username		You did not read Lemma 1.2 correctly. Read it again (suppose further..).
Dec 10, 2021 at 10:46	comment	added	Mr.xue		@username Thanks for your reply. I think your idea is helpful to solve this question. However, I also don't know how to complete the rest part of the proof.
Dec 10, 2021 at 9:54	comment	added	username		Here is a.n idea. Suppose $n=2^k\Leftrightarrow k = \ln n/\ln2$. Then $$ \gamma(n)\leq 2C\gamma(2^{k-1})\leq \cdots \leq 2^k C^k = n C^{\ln n/\ln2} =n^{1+\ln C/\ln2}. $$ It doesn't show $t^2$, but it shows no larger than $t^{1+\frac{\ln C}{\ln 2}}$. Is that enough?
Dec 10, 2021 at 8:19	history	edited	YCor	CC BY-SA 4.0	changed tag, formatting
Dec 10, 2021 at 8:10	history	asked	Mr.xue	CC BY-SA 4.0