By L. Auslander, R. Tolimieri
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Extra resources for Abelian Harmonic Analysis, Theta Functions and Functional Analysis on a Nilmanifold
1 n(p--1)iZ, Take Vx, t(y) = t l' -n fEY(p) E t( 1 O
O Ig(x, t) I ;:; C (J 1 (x) + J 2 (x) + J 3 (x)) where sup t tI < t xl -n J \f(y)j dy, Iy- xI ;:; t 26 27 EMBEDDING AND MULTIPLIER THEOREMS FOR Hp(Rn) 1 N = n(p - 1) For we also need two other estimates. J)N- 1 lxl -n J ' lxl (J 6 (x) + \If\\ 1 > , L -n dx, p= 1 , where J6(x) t sup t-n <1 J lf(y)l dy.
3). 8) follows BAERNSTEIN AND SAWYER 50 dx ( 6. 4) we have 0 E ... E + = A(x) + B(x) j = 1 j =-
2) 43 BAERNSTEIN AND SAWYER 44 1 where n(-- l),p X = K1 P for 0
0 be given. 3) • Then (a) if (b) The constants depend only on C j~O, p,n, and r This lemma, and the next one, will be proved at the end of the section.
Abelian Harmonic Analysis, Theta Functions and Functional Analysis on a Nilmanifold by L. Auslander, R. Tolimieri