Pseudo-multipliers and smooth molecules on Hermite Besov and Hermite\n Triebel--Lizorkin spaces

2020/01/31 by Fu Ken Ly, Ly, Fu Ken, Virginia Naibo +1
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2002.00112

openalex publication_date 2020/01/31 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We obtain new molecular decompositions and molecular synthesis estimates for\nHermite Besov and Hermite Triebel--Lizorkin spaces and use such tools to prove\nboundedness properties of Hermite pseudo-multipliers on those spaces. The\nnotion of molecule we develop leads to boundedness of pseudo-multipliers\nassociated to symbols of H "ormander-type adapted to the Hermite setting on\nspaces with non-positive smoothness; in particular, we obtain continuity\nresults for such operators on Lebesgue and Hermite local Hardy spaces. As a\nbyproduct of our results on boundedness properties of pseudo-multipliers, we\nshow that Hermite Besov spaces and Hermite Triebel--Lizorkin spaces are closed\nunder non-linearities.\n

Related

• The Molecular Characterizations of Variable Triebel-Lizorkin Spaces Associated with the Hermite Operator and Its Applications
• Matrix-Weighted Besov-Type and Triebel--Lizorkin-Type Spaces III: Characterizations of Molecules and Wavelets, Trace Theorems, and Boundedness of Pseudo-Differential Operators and Calderón--Zygmund Operators
• Decomposition of spaces of distributions induced by Hermite expansions
• Besov--Triebel--Lizorkin-Type Spaces with Matrix A_∞ Weights
• Wavelet Characterization of Besov and Triebel--Lizorkin Spaces on Spaces of Homogeneous Type and Its Applications