On the composition operators on Besov and Triebel-Lizorkin spaces of power weights

2021/08/02 by Douadi Drihem, Drihem, Douadi
Mathematics · #46E35 #47H30 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2108.00718

openalex publication_date 2021/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G:\mathbbR→ R be a continuous function. Under some assumptions on G, s,α,p and q we prove that \G(f):f∈ A_p,q^s(ℝⁿ,|⋅ |^α)\⊂ A_p,q^s(ℝⁿ,|⋅ |^α) implies G is a linear function. Here A_p,q^s(ℝⁿ,|⋅|^α) stands for either the Besov space B_p,q^s(ℝⁿ,|⋅ |^α) or the Triebel-Lizorkin space F_p,q^s(ℝⁿ,|⋅ |^α). These spaces unify and generalize many classical function spaces such as Sobolev spaces of power weights. One of the main difficulties to study this problem is that the norm of the A_p,q^s(ℝⁿ,|⋅ |^α) spaces with α≠ 0 is not translation invariant, so some new techniques must be developed.

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