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 .