Function Spaces, Differential Operators and Nonlinear by Herbert Amann (auth.), Prof. Dr. Hans-Jürgen Schmeisser,

By Herbert Amann (auth.), Prof. Dr. Hans-Jürgen Schmeisser, Prof. Dr. Hans Triebel (eds.)

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We also put X E JRn , k = 2, 3, .... 31 Then the sequence (

3) if s rt. z' if s E Z. 4) Thus Hölder spaces are kind of 'universal' multiplier spaces for ofp. 8) Of course, JE"(n) depends on er too for a E (0, 1)\{1/2}. We choose a boundary characterization map 6 and define scales of boundary spaces aw;, 1

Jawerth and M. Milman (cf. [JaM91]) which is of an entirely different nature than the one considered here. 1 Remarks {a) Of course, we can replace in the above procedure Ao by A-1 and construct the 39 interpolation-extrapolation scale {(Fa, Ba) ; -1 :S a < oo} over [-1, oo) generated by A_l and ~- Then { (Fa+l,Ba+I); a ~ -1} is naturally isomorphic to { ( E 01 , A 01 ) ; a ~ -1 } . 4) to a scale over [-2,oo), { (E 01 , Aa) ; -2 :S a < 00} . By repeating this argument, given any m E W, we can construct the interpolationextrapolation scale over [-m, oo) generated by A 0 and ~' { (E 01 , Aa) ; -m :S a < oo} .

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