A Kind Of Equivalent Characterization Of The F(p,q,s)space On The Unit Ball And Integral Estimates On The Surface Of The Unit Ball

In this dissertation,we first discuss the fractional derivative characterization and atomic decomposition of the F(p,q,s)space on the unit ball.The equivalent characterization with the generalized fractional derivative form of the F(p,q,s)space is given.At the same time,we give a kind of sufficient condition of atomic decomposition for the functions on the F(p,q,s)space.That is,infinite linear combinations with coefficients satisfying certain conditions and similar to kernel functions belong to the F(p,q,s)space.Secondly,we discuss the bidirectional estimates of the surface integral with two variable points in the unit ball,and the bidirectional estimates for all 11 cases are given.This dissertation consists of three chapters.In the first chapter,we give a comprehensive summary about the research background and the conclusions that we obtain.In the second chapter,we give equivalent characterization with the generalized fractional derivative form of the F(p,q,s)space on the unit ball,that is theorem 2.3.1.At the same time,a kind of sufficient condition of atomic decomposition for the functions on the F(p,q,s)space in the unit ball is given,that is theorem 2.3.2.In the third chapter,we give the bidirectional estimates of the surface integral with two variable points in the unit ball for all 11 cases,that is theorem3.3.1.