EMBEDDING AND MULTIPLIER THEOREMS FOR HP(Rn)
STANDING NOTATION
(0.1) N denotes the largest integer less than or equal to n(— - 1) .
(0.2) A^ denotes the shell jx £ Rn : 2 |xj 2 + J, k £ Z .
(0.3) HP = HP(Rn) .
(0.4) ff = J * f(x)dx
y
and dx denotes Lebesgue measure on R
R
(0.5) C denotes a constant depending possibly on n and p which can
change from line to line.
(0.6) For x £ R
9
x. denote the coordinates of x .
(0.7) We use the usual multi-index notation. For ( 3 = (£. , . . .,3 ) with
1 n
each (3. a non-negative integer^
x =
Xl
N
(0.8) For f £ C , P f denotes the N'th Taylor polynomial of f with
basepoint x = 0 .
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