Some results on variable Gaussian Besov-Lipschitz and variable Gaussian Triebel-Lizorkin spaces

2021/09/20 by Ebner Pineda, Luz Rodríguez, Pineda, Ebner +3
Mathematics · #42B35 #47G1 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration #Primary 42B25 #Secondary 46E30

paper · pdf · doi:10.48550/arxiv.2109.09288

openalex publication_date 2021/09/20 · openalex created_date 2021/09/27 · openalex updated_date 2026/07/28

Abstract

In a previous paper two of the authors introduced and study Gaussian Besov-Lipschitz spaces B_p,q^α(γ_d) and Gaussian Triebel-Lizorkin spaces F_p,q^α(γ_d). Now, in this paper we introduce the variable Gaussian Besov-Lipschitz spaces B_{p(⋅),q(⋅)}^α(γ_d) and the variable Gaussian Triebel-Lizorkin spaces F_{p(⋅),q(⋅)}^α(γ_d), that is to say, Gaussian Besov-Lipschitz and Triebel-Lizorkin spaces with variable exponents, under certain additional regularity conditions on the exponents p(⋅) and q(⋅) introduced by Dalmasso and Scotto. Trivially, they include the Gaussian Besov-Lipschitz spaces B_p,q^α(γ_d) and Gaussian Triebel-Lizorkin spaces F_p,q^α(γ_d). We consider some inclusion relations of those spaces and finally we also prove some interpolation results for them.

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