Timeline for Example of a function with a curious property
Current License: CC BY-SA 4.0
8 events
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| Aug 16, 2020 at 7:45 | comment | added | Giorgio Metafune | A similar argument: once $F(0)=0$ has been proved, then $F(x)=\int_0^x F'(t)dt$ and $$\int_0^1 \frac{|F(x)|}{x^2}dx\le \int_0^1 \frac{1}{x^2} dx\int_0^x |F'(t)|dt=\int_0^1 |F'(t)|dt \int_t^1 x^{-2}dx=\int_0^1 |F'(t)|\frac{1-t}{t}dt$$. | |
| Aug 15, 2020 at 23:33 | comment | added | Fedor Petrov | @LSpice yes, now added | |
| Aug 15, 2020 at 23:33 | history | edited | Fedor Petrov | CC BY-SA 4.0 |
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| Aug 15, 2020 at 23:13 | comment | added | LSpice | You’re proving that the answer to the stated question (does there exist $F$ such that $F(x)/x \in L^1$, $F’(x)/x \in L^1$, $F(x)/x^2 \notin L^1$) is “no”, right? | |
| Aug 15, 2020 at 23:12 | history | edited | Fedor Petrov | CC BY-SA 4.0 |
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| Aug 15, 2020 at 23:03 | vote | accept | Tony419 | ||
| Aug 15, 2020 at 23:03 | comment | added | Tony419 | Cool, thanks! :] | |
| Aug 15, 2020 at 22:59 | history | answered | Fedor Petrov | CC BY-SA 4.0 |