ABSTRACT
In the following lemmas f, g denote functions in S(Rn ). The extension of these results to functions for which the right-hand side of (2.2)-(2.4) make sense is standard.
(2.2)
PROOF: When s is a positive integer, the above result is well known. The case 0 < s < 1 was proved by R. S. Strichartz ([23], Theorem 2.1, Chapter 2). For the proof of the general case we refer to T. Runst ([20], p. 332), and T. Kato and G. Ponce ([17] Appendix, Lemma X4). In [20] the spaces Ff•q used there coincide with the spaces L~ when q = p. I would like to thank Prof. R. S. Strichartz for pointing out to me this reference.
