Composition operators on Herz-type Triebel-Lizorkin spaces with application to semilinear parabolic equations

2022/01/16 by Douadi Drihem, Drihem, Douadi
Computer Science · Mathematics · #35K45 #35K55 #46E35 #47H30 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2201.06055

openalex publication_date 2022/01/16 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

Let G:\mathbbR→ R be a continuous function. In the first part of this paper, we investigate sufficient conditions on G such that \G(f):f∈ K_p,q^αF_β^s\⊂ K_p,q^αF_β^s holds. Here K_p,q^αF_β^s are Herz-type Triebel-Lizorkin spaces. These spaces unify and generalize many classical function spaces such as Lebesgue spaces of power weights, Sobolev and Triebel-Lizorkin spaces of power weights. In the second part of this paper we will study local and global Cauchy problems for the semilinear parabolic equations ∂ _tu-Δu=G(u) with initial data in Herz-type Triebel-Lizorkin spaces. Our results cover the results obtained with initial data in some know function spaces such us fractional Sobolev spaces. Some limit cases are given.

Related

• On the composition operators on Besov and Triebel-Lizorkin spaces of power weights
• Sobolev embeddings for Herz-type Triebel-Lizorkin spaces
• Second Order Operators Subject to Dirichlet Boundary Conditions in Weighted Triebel-Lizorkin Spaces: Parabolic Problems
• Composition operators on function spaces on the halfplane: spectra and semigroups
• Wavelets and Triebel type oscillation spaces