2023/05/20 by Jian Tan, Tan, Jian · 1 citation
Mathematics · Social Sciences · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Polish Historical and Cultural Studies #Polish Legal and Social Issues
paper · pdf · doi:10.48550/arxiv.2305.12227
openalex publication_date 2023/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main purpose of this paper is to develop the theory of product Hardy spaces built on Banach lattices on \mathbb Rn×\mathbb Rm. First we introduce new product Hardy spaces HX(\mathbb Rn×\mathbb Rm) associated with ball quasi-Banach function spaces X(\mathbb Rn×\mathbb Rm) via applying the Littlewood-Paley-Stein theory. Then we establish a decomposition theorem for HX(\mathbb Rn×\mathbb Rm) in terms of the discrete Calderón's identity. Moreover, we explore some useful and general extrapolation theorems of Rubio de Francia on X(\mathbb Rn×\mathbb Rm) and give some applications to boundedness of operators. Finally, we conclude that the two-parameter singular integral operators \widetilde T are bounded from HX(\mathbb Rn×\mathbb Rm) to itself and bounded from HX(\mathbb Rn×\mathbb Rm) to X(\mathbb Rn×\mathbb Rm) via extrapolation. The main results obtained in this paper have a wide range of generality. Especially, we can apply these results to many concrete examples of ball quasi-Banach function spaces, including product Herz spaces, weighted product Morrey spaces and product Musielak--Orlicz--type spaces.