Theory of Singular Integral Operators in Non-commutative Harmonic Analysis. A verification of Use of Real Hardy Spaces.

点击翻译按钮获取中文摘要

In the past 4 years from 2008 to 2011 real Hardy spaces for Jacobi analysis and their atomic decompositions have been investigated. Moreover, as applications of the Hardy spaces, Lp boundedness of some singular integral operators and the theory of interpolation spaces were established. These results for the spaces of non-homogeneous type are natural extension of ones in the Euclidean spaces and the Dunkl analysis,. Jacobi analysis is a special case of Chebli-Trimeche hypergroups. As ancillary research, several uncertainty principles are also obtained for the spaces of non-homogeneous type. These results obtained in this research pave the way to harmonic analysis for the Cherednik transform.