We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Hardy Spaces Associated with Monge-Ampère Equation.
- Authors
Han, Yongshen; Lee, Ming-Yi; Lin, Chin-Cheng
- Abstract
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.
- Publication
Journal of Geometric Analysis, 2018, Vol 28, Issue 4, p3312
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/s12220-017-9961-6