Timeline for Real interpolation for vector-valued Sobolev spaces
Current License: CC BY-SA 4.0
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| Apr 22, 2022 at 20:31 | history | edited | Theleb | CC BY-SA 4.0 |
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| Apr 22, 2022 at 20:22 | vote | accept | Theleb | ||
| Apr 22, 2022 at 10:07 | answer | added | Hannes | timeline score: 4 | |
| Apr 22, 2022 at 9:05 | history | edited | Theleb | CC BY-SA 4.0 |
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| Apr 6, 2022 at 14:43 | history | edited | Theleb | CC BY-SA 4.0 |
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| Apr 6, 2022 at 14:40 | comment | added | Theleb | That is a good question. I didn't really think about it until now. I think I would have naturally opted for the definition with a Fourier transform approach with the multiplier $\xi \mapsto (1+|\xi|^2)^{\theta/2}$. Are you refering to the so called Lizorkin-Triebel spaces $F^s_{p,q}$ ? Thank you for your remark, indeed i am in the diagonal case. | |
| Apr 6, 2022 at 13:23 | comment | added | Willie Wong | How is the vector valued Sobolev space $W^{\theta,p}(0,T;X)$ defined? (I ask because the sequence space version of the interpolation you want $(\ell^{0}_q(X_1),\ell^{1}_q(X_2))_{\theta,q} = \ell^{\theta}_q((X_1, X_2)_{\theta,q})$ is true, and so if you have a Littlewood Paley type representation of the vector-valued Sobolev spaces the same way you do for the scalar ones, then the result should hold.) // Incidentally, the paper you linked to is about the non-diagonal case of the interpolation; the result that you desire is firmly in the diagonal case (all 4 occurrences of $p$ agree). | |
| Apr 5, 2022 at 13:20 | history | asked | Theleb | CC BY-SA 4.0 |