### Theory of Trees and a Local T(1) Theorem

By Yumeng Ou

November 6, 2012

#### Abstract

Theory of trees in harmonic analysis has played a significant role in the study of bilinear singular integrals. And although it is a more recent technique compared with the theory of Carleson measure and related objects, those two are actually closely connected. I will introduce some basic results in a framework that unifies both of them together, and show how this technique can be used to prove a local T(1) theorem. If there is time, I may also talk about something about the more generalized local T(b) theorem as well.