Function Spaces of Lizorkin-triebel Type with Exponential Weights

Let S = S(R n) be the Schwartz space of all rapidly decreasing C 1 functions. All function spaces that occur here are deened on R n. Therefore, we omit the suux R n in S(R n) as well as in the other spaces below. Let D be the space of all compactly supported C 1 functions equipped with the usual topology. By S 0 and D 0 we denote the strong topological dual spaces of S and D, respectively. For 0 < p < 1, L p are the usual Lebesgue spaces. If u is a weight function, i.e., measurable and positive a.e. with respect to the Lebesgue measure on R n , then L p (u) is equipped with the norm kf j L p (u)k = kuf j L p k. To each function ' 2 S we assign its Fourier transform b '(x) = (2) ?n=2