Criterion of Boundedness of Singular Integrals and H\"older Space on Spaces of Homogeneous Type
报告题目(Title)：Criterion of Boundedness of Singular Integrals and H\"older Space on Spaces of Homogeneous Type
报告人(Speaker)：Prof. Yongsheng Han (Auburn University)
It was well known that geometric considerations enter in a decisive way in many questions of harmonic analysis. In this talk, we describe the criterion of the boundedness for singular
integrals on the H\¨older space and, as an application, new proof of the T1 theorem is given on spaces of homogeneous type $(X, d, \mu)$ in the sense of Coifman and Weiss, where the quasimetric $d$ may have no regularity and the measure μ satisfies the doubling property only. We make no additional geometric assumptions on the quasi-metric or the doubling measure and thus, these results extend to the full generality of all related previous ones, in which the extra geometric assumptions were made on both the quasi-metric d and the measure $\mu$. To achieve our goal, a crucial idea is to introduce a new wavelet-type decomposition which involves a new quasi-metric $d'$ that is geometrically equivalent to the original quasi-metric $d$. Moreover, the wavelet-type functions in this decomposition have the compact supports.