Complex interpolation of function spaces with general weights

Abstract

In this paper, we present the complex interpolation of Besov and Triebel-Lizorkin spaces with generalized smoothness. In some particular cases these function spaces are just weighted Besov and Triebel-Lizorkin spaces. An application, we obtain the complex interpolation between the weighted Triebel-Lizorkin spaces Ḟ s0 p0,q0 (ω 0 ) and Ḟ s1 ∞,q1 (ω 1 ) with suitable assumptions on the parameters s 0 , s 1 , p 0 , q 0 and q 1 , and the pair of weights (ω 0 , ω 1 ).

Triebel–Lizorkin spaces with general weights

“…Allowing the smoothness t k , k ∈ Z to vary from point to point will raise extra difficulties to study these function spaces. But by the following lemma the problem can be reduced to the case of fixed smoothness, see [9]. Proposition 3.12.…”

Triebel-Lizorkin spaces with general weights

“…Allowing the smoothness t k , k ∈ Z to vary from point to point will raise extra difficulties to study these function spaces. But by the following lemma the problem can be reduced to the case of fixed smoothness, see [16].…”

“…Other properties of these function spaces such as duality, the case p = ∞ and complex interpolation are given in [15] and [16].…”