Strengthen Posedness In The Binary Decomposition And The Initial Value Of The Reign Of Potential Space And Besov Space

Dyadic Decomposition is delicate and deep thought in harmonic analysis, Besov Space and Triebel spaces are the mutual interaction between dyadic decomposition andlq(Lp), Lp(lq).And then we studied the well-Posedness of some equations in those spaces.But the Dyadic Decomposition estimate which make the scope of P in the Strichartz estimate been greatly reduced.In the 1930s, N.Wiener[9] used the concept of Frequency-uniform decomposition [5] [6] [7] [8] make those thought develop.By Frequency-uniform decomposition,they made two original question was optimized:1, Berstein Estimate for the better,from then weBut there are also some flaws in Frequency-uniform decomposition, for example, its this estimate:1, only for S1(t)= eit|ξ|m,but for Dyadic decomposition we have considered all of the radial func-tion.By mutual interaction between Frequency-uniform decomposition and lq (Lp),modulation space is constructed.But when we discuss the well-posedness in this space,the scop of q is greatly reduced relative to Besov space.To solve these problems,our article focus on is to construct a new decomposition.(in this article, we recorded as (?)),At the same time combining this decomposition and con-struct a new space(in this article, we recorded as Mp,qs).And then discuss the Well-posedness problems in this space.Not only to solve the drawbacks of frequency-uniform decompo-sition while preserving the advantages by introduce frequency-uniform decomposition Keywords:Dyadic Decomposition,Frequency-uniform decomposition, stronger Dyadic Decomposition, Besov Space, Triebel Space, Strichartz estimate...