Boundedness Of Two Operators On Herz Type Spaces

It is well known that with the rapid development of harmonic analysis and paradif-ferential equation,there connection are more and more closer. For example,in the studyof paradifferential equations ,the method of harmonic analysis has become an impor-tant problem. With the application of harmonic analysis in paradifferential equations,thepesudo-differential operators and multiplication operators are two useful tools. The use ofpesudo-differential operators especially reflect in the nonlinear pesudo-differential equa-tions. While multiplication operators often appear in the Navier-Stokes equations andsome Kinetic equations. So the study of these operators is helpful to get estimate ofequations solution.Chapter 1 presents the background and gives some necessary notations as well asdefinitions of spaces.Chapter 2 estimates the pseudo-differential operators with Herz-type Besov norm.Chapter 3 estimates the boundedness of the multiplication operators with Herz-typeSobolev norm.Chapter 4 proves bilinear estimation for the multiplication operators in the Herz-typeTriebel-Lizorkin space.