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May 31 at 9:49 comment added Willie Wong I don't understand your follow up question. What exactly do you mean by a "direct proof"? Tomas' proof is only 1 paragraph long and the only advanced machinery invoked is interpolation theory. I do not know any proofs of the restriction theorem without using some interpolation.
May 31 at 6:11 comment added Edward Is there a direct proof to prove $\int_{\mathbb{S}^{n-1}} |\hat{f}(\omega)|^2 ~d\omega<\infty$
May 31 at 6:10 comment added Edward Thank you for your reference.
May 30 at 23:35 history answered Willie Wong CC BY-SA 4.0