Timeline for Ratio of the constants of the Marcinkiewicz–Zygmund inequality for p=1
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Nov 23, 2023 at 9:58 | vote | accept | allsisyphus | ||
| Nov 16, 2023 at 14:23 | comment | added | Iosif Pinelis | @allsisyphus : You are welcome! I have now added to the answer a response to your comment. Briefly, no better factors can be obtained even for reasonable small classes of r.v.'s. | |
| Nov 16, 2023 at 14:20 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 16, 2023 at 14:01 | comment | added | Iosif Pinelis | @LSpice : Thank you for your edits. They were probably removed accidentally, as I edited in an offline editor a version of the answer preceding your edits. | |
| Nov 16, 2023 at 8:52 | comment | added | allsisyphus | Thank you very much! If I well understood such constants are the best ones in the sense that for each bound it is possible to provide (independent and zero-mean) variables that saturate that bound, am I right? If so, is there any know families of r.v. where such best constant are known to be different from that of the larger class? | |
| Nov 16, 2023 at 8:12 | comment | added | Giorgio Metafune | Thank you very much, now it is clear to me. | |
| Nov 16, 2023 at 3:13 | comment | added | LSpice |
I guess I can understand preferring \ldots to \dotsc, and I apologise for an unwelcome edit, but why remove the name of the Haagerup paper ("The best constants in the Khintchine inequality")?
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| Nov 16, 2023 at 2:12 | comment | added | Iosif Pinelis | @GiorgioMetafune : I have added details on the conditioning. Please let me know if more details are needed. | |
| Nov 16, 2023 at 2:10 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 15, 2023 at 22:42 | comment | added | Giorgio Metafune | However, could you explain in more detail how to reduce the symmetric case to the Rademacher functions? | |
| Nov 15, 2023 at 22:04 | comment | added | Giorgio Metafune | I see why: $|x+y|^p-|x|^p \geq p|x|^{p-2} xy$ which follows from the convexity of $|x|^p$. | |
| Nov 15, 2023 at 21:46 | comment | added | Giorgio Metafune | Why $E|S_X|^p \leq E|S_X-S_{X'}|^p$ and similar? | |
| Nov 15, 2023 at 18:15 | history | edited | LSpice | CC BY-SA 4.0 |
Title of Haagerup paper
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| Nov 15, 2023 at 18:11 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 15, 2023 at 18:04 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 15, 2023 at 17:49 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |