I am taking a graduate Harmonic Analysis course without having taken a Functional Analysis course (supposed to take it next semester). I have done fine by reading up on whatever odds and bits I have needed but a common manner of proof is proving something on the Schwarz space (or some other dense subspace) and extending to $L^P$ space. I haven't seen these before so I am hoping I can be directed to some reference material with perhaps some prototypical examples of such proofs. Cheers.
2026-04-12 16:59:15.1776013155
Proving something on the Schwarz space and extending to $L^p$ space
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