Timeline for Boundedness of Riesz potential on Hardy space
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Sep 17, 2020 at 15:38 | comment | added | Slm2004 | I think you are right. Now I believe the claim of the paper should be if $(-\Delta)^{\frac14}u\in L^{2,\infty}\cap L^p$ for some $1\leq p<\infty$ then $u\in BMO$. The claim implicitly uses $I_{1/2}v$ is a locally integrable function for $v=(-\Delta)^{1/4}u$. | |
| Sep 17, 2020 at 4:33 | comment | added | Piero D'Ancona | Let $v=(-\Delta)^{1/4}u$. The claim of the paper states that if $v\in L^{2,\infty}$ then $(-\Delta)^{-1/4}v\in BMO$. Is this the claim or not? | |
| Sep 16, 2020 at 13:14 | comment | added | Slm2004 | Thank you for your answer. However, I believe the claim is right. It says about if $u\in \mathcal{H}^1$ then $I_{1/2}u\in L^{2,1}$. Only those $v\in L^{2,\infty}$ can be written as $(-\Delta)^{\frac14}u$ can have $I_{1/2}v\in BMO$. Do you have counter example of $u\in \mathcal{H}^1$? | |
| Sep 16, 2020 at 11:37 | history | answered | Piero D'Ancona | CC BY-SA 4.0 |