Harmonic Analysis And Related Issues

Harmonic analysis, which has profound history background and rich theory, is one of the most important branches in mathematics, and has been extensively applied in almost all fields of mathematics,such as partial differential equation and geometry analysis.The thesis will study the harmonic analysis and also its application of partial differential equation and geometry analysis. It is divided into four chapters: In chapter 1, we study the boundedness of a class of singular integral operators in weighted Hardy spaces. In chapter 2,we conside the short time solutions of Euler equations in the endpoints of Besov spaces. In chapter 3,we gain the conditions of Navier-stokes equations' regularity and blow-up. In chapter 4,we consider the existence of harmonic function in negative sectional curvature manifolds.we get that,if Ricci(x) ≥ -C(1 + r~2)(r = ρ(O.x)), then there have non-canstant bounded harmnic function in negative sectional curvature manifolds.In the following, we will state the main content of every chapter.Chapter 1 Suppose ω∈A_q,q ≥ 1.let φ∈ S(Schwartz function space),∫φ=...