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Mar 2, 2021 at 20:25 history edited B K CC BY-SA 4.0
Added paragraph on the uniform boundedness in Sobolev spaces
Mar 2, 2021 at 20:04 comment added B K @CarlosEsparza: $(1-\Delta)^{r/2}$ is defined using the functional calculus for unbounded symmetric operators. Here $-\Delta$ is non-negative and has a canonical self-adjoint extension called Friedrichs extension. For the uniform boundedness on the Sobolev spaces I'll add a pagragraph to my answer.
Mar 1, 2021 at 19:41 comment added Carlos Esparza But I don't see how you get uniform boundedness in $\epsilon$...
Mar 1, 2021 at 19:40 comment added Carlos Esparza So you're basically using that the operator $(1 - \Delta)^{r/2}$ (defined by some functional calculus I suppose) is an isometry between $W^r$ and $L^2$?
Mar 1, 2021 at 19:37 history bounty ended Carlos Esparza
Feb 21, 2021 at 20:20 history answered B K CC BY-SA 4.0