The following is an excerpt from Folland's Real Analysis:
Would anybody elaborate why the estimate in the first box implies the second and third boxes?
2026-04-19 13:00:38.1776603638
Fourier transform and the Sobolev space $H_k$ in Folland's Real Analysis
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Thanks to user1952009's comment, the first box itself does not imply the later two boxes. One would have the conclusions by looking at the Fourier transform of $\partial^\alpha f$ and applying the Plancherel Theorem.