Hardy Spaces Associated with Monge–Ampère Equation

研究成果: 雜誌貢獻期刊論文同行評審

1 引文 斯高帕斯(Scopus)


The main concern of this paper is to study the boundedness of singular integrals related to the Monge–Ampère equation established by Caffarelli and Gutiérrez. They obtained the L2 boundedness. Since then the Lp, 1 < p< ∞, weak (1,1) and the boundedness for these operators on atomic Hardy space were obtained by several authors. It was well known that the geometric conditions on measures play a crucial role in the theory of the Hardy space. In this paper, we establish the Hardy space HFp via the Littlewood–Paley theory with the Monge–Ampère measure satisfying the doubling property together with the noncollapsing condition, and show the HFp boundedness of Monge–Ampère singular integrals. The approach is based on the L2 theory and the main tool is the discrete Calderón reproducing formula associated with the doubling property only.

頁(從 - 到)3312-3347
期刊Journal of Geometric Analysis
出版狀態已出版 - 15 12月 2018


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