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Download e-book for kindle: Abelian Harmonic Analysis, Theta Functions and Functional by L. Auslander, R. Tolimieri

By L. Auslander, R. Tolimieri

ISBN-10: 0387071342

ISBN-13: 9780387071343

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Extra resources for Abelian Harmonic Analysis, Theta Functions and Functional Analysis on a Nilmanifold

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1 n(p--1)iZ, Take Vx, t(y) = t l' -n fEY(p) E t( 1 OO 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 =-4 I B(x) I dx ~ ... E j =1 J I xj > 2 ... l k=j+2 ~ J J j::::_1 , and suppose that x E ~. (x) = J J rIYl < 2k - 1 .. 16) that ~ 1 I: J(k,j) ~w(j) k=j+l 1 I: w(k) J(k,j) ~w(j), k=j+l m j~O. BAERNSTEIN AND SAWYER 52 Hence . 21) The proof of (6,20) is postponed temporarily. 21) to the Let R(s) = 2J.. e-elsl inequality we need. where e >0 and Is I Then IIR*all 1 ~ C We will show now how to j E P, ...

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.

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Abelian Harmonic Analysis, Theta Functions and Functional Analysis on a Nilmanifold by L. Auslander, R. Tolimieri


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