Cauchy-Szegö projections and related topics
Applicable Nonlinear Analysis, Volume 1, Issue 2, December 2024, Pages: 110–159
DER-CHEN CHANG
Department of Mathematics and Statistics, Georgetown University, Washington DC, 20057, USA
Graduate Institute of Business Administration, College of Management, Fu Jen Catholic University, New Taipei City 242, Taiwan, ROC
XINFENG WU
Department of Mathematics, China University of Mining and Technology, Beijing 100083, P. R. China
JEN-CHIH YAO
China Medical University, Taichung, 406040, Taiwan, ROC
Academy of Romanian Scientists, 50044 Bucharest, Romania
Abstract
In this survey article, we give a comprehensive review of Calderón-Zygmund operators from ´ the point of view of Cauchy-Szegö projections and the sharp estimates of the operators in Hardy spaces. ¨ Cauchy-Szegö projections is closed related to the Hilbert transform which is a typical example of the so- ¨ called “first generation” of singular integral operators and has been studied by mathematicians for many years, We started with the case in unit disk \(\mathfrak D_1\) in \(\mathfrak C_1\) and then move to the unbounded unit ball \(\mathfrak B_{n+1}\) in \(\mathfrak C_{n+1}\). Analysis on Rn and Hn are quite different. We try to explain the idea behind it carefully.
Cite this Article as
Der-Chen Chang, Xinfeng Wu, and Jen-Chih Yao, Cauchy-Szegö projections and related topics, Applicable Nonlinear Analysis, 1(2), 110–159, 2024