Endpoint Estimates For Severial Operators With Nondoubling Measures

In recent years, many papers pay attention to the study of non-doubling measuresin harmonic analysis. Recently it has proved that a big part of the classical Calderón-Zygmund operator theory remains valid if the doubling assumption onμis replaced bythe growth condition, namely, there exist a constant C₀ > 0 such thatμ(B(x,r))≤C₀rⁿ,for all x∈R^d and r > 0, where n is a fixed number and 0 < n≤d.This thesis aims to study the the boundedness of Calderón-Zygmund operator onnon-doubling measures. The thesis comprises three chapters.Chapter 1 presents the background and gives some necessary notations as well asdefinitions of spaces.The purpose of Chapter 2 is devoted to estimate the boundedness of the maximalCalderón-Zygmund singular integral operator in the RBLO spaces.In Chapter 3, we proceed to estimate the boundedness of theθ(t) type Calderòn-Zygmund Operators in the RBMO spaces.