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yesterday comment added John_zyj This problem can be generalized, the details are described here (mathoverflow.net/questions/484304/…). I turn to you for assistance. Thank you!
Aug 1 at 18:35 comment added John_zyj Very concise and elegant proof! Thank you!
Aug 1 at 18:30 vote accept John_zyj
Aug 1 at 17:26 history edited Fedor Petrov CC BY-SA 4.0
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Aug 1 at 15:16 comment added Fedor Petrov Please check another attempt, with another answer. I am not certain about proofs, but at least one of two answers is correct.
Aug 1 at 15:14 history undeleted Fedor Petrov
Aug 1 at 15:14 history edited Fedor Petrov CC BY-SA 4.0
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Aug 1 at 14:56 history deleted Fedor Petrov via Vote
Aug 1 at 13:34 comment added John_zyj Thank you for your reply! But I think $T$ should be less than $1$. Since $\frac{1}{\sigma}<1$, so $\frac{1}{\sigma}-1<0$, and therefore $T=R^{\frac{1}{\sigma}-1}<1$. So the inequality to be proven is true when $\sigma=1$.
Aug 1 at 5:45 history answered Fedor Petrov CC BY-SA 4.0