2022/04/26 by Yirui Zhao, Dachun Yang, Zhao, Yirui +3
Mathematics · #42B30 #46E30 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary 42B35 #Secondary 42B25
paper · pdf · doi:10.48550/arxiv.2204.12019
openalex publication_date 2022/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, the authors introduce a class of mixed-norm Herz spaces, E^α,p_q(ℝn), which is a natural generalization of mixed Lebesgue spaces and some special cases of which naturally appear in the study of the summability of Fourier transforms on mixed-norm Lebesgue spaces. The authors also give their dual spaces and obtain the Riesz-Thorin interpolation theorem on E^α,p_q(ℝn). Applying these Riesz-Thorin interpolation theorem and using some ideas from the extrapolation theorem, the authors establish both the boundedness of the Hardy-Littlewood maximal operator and the Fefferman-Stein vector-valued maximal inequality on E^α,p_q(ℝn). As applications, the authors develop various real-variable theory of Hardy spaces associated with E^α,p_q(ℝn) by using the existing results of Hardy spaces associated with ball quasi-Banach function spaces. These results strongly depend on the duality of E^α,p_q(ℝn) and the non-trivial constructions of auxiliary functions in the Riesz-Thorin interpolation theorem.