It's true this Sobolev spaces embedding?
if $ k < s $ then $ H^{s}(R^n)\hookrightarrow H^{k}(R^n) $ ?
Thank you.
It's true this Sobolev spaces embedding?
if $ k < s $ then $ H^{s}(R^n)\hookrightarrow H^{k}(R^n) $ ?
Thank you.
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Yes. This is a direct consequence of the $H^s$ norm being stronger than the $H^k$ norm for $s>k$.