Oscillations and differences in Triebel-Lizorkin-Morrey spaces

2023/06/27 by Marc Hovemann, Hovemann, Marc, Markus Weimar +1 · 1 citation
Mathematics · #26B35 #41A30 #46E30 #46E35 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2306.15239

openalex publication_date 2023/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we are concerned with Triebel-Lizorkin-Morrey spaces E^s_u,p,q(Ω) of positive smoothness s defined on (special or bounded) Lipschitz domains Ω⊂ℝ^d as well as on ℝ^d. For those spaces we prove new equivalent characterizations in terms of local oscillations which hold as long as some standard conditions on the parameters are fulfilled. As a byproduct, we also obtain novel characterizations of E^s_u,p,q(Ω) using differences of higher order. Special cases include standard Triebel-Lizorkin spaces F^s_p,q (Ω) and hence classical L_p-Sobolev spaces H^s_p(Ω). Key words: Triebel-Lizorkin-Morrey space, Morrey space, Lipschitz domain, oscillations, higher order differences

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• On the boundedness of dilation operators in the context of Triebel-Lizorkin-Morrey spaces

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