On the duality of variable Triebel–Lizorkin spaces

Abstract

The aim of this paper is to prove duality of Triebel-Lizorkin spaces F α(·) 1,q(·) . First, we prove the duality of associated sequence spaces. Then from the so-called ϕ-transform characterization in the sense of Frazier and Jawerth, we deduce the main result of this paper.MSC 2010 : 46B10, 46E35.

Complex interpolation of variable Triebel–Lizorkin spaces

“…For more information about these function spaces, consult [5] and [6], with different notation. Notice that the supremum can be taken respect to dyadic cubes with side length ≤ 1.…”

“…By [10, pp. 130-131], there exist functions Ψ ∈ S(R n ) satisfying (5) and ψ ∈ S(R n ) satisfying (6)…”