Linear Average And Stochastic Widths Of Weighted Besov Spaces

In this paper, we investigate the asymptotic degrees of linear average and stochastic widths of embeddings of weighted Besov spaces in the average setting and randomized setting. This thesis is organized as follows.In the first chapter, the background and significance of the research are presented. We also introduce some basic symbols, concepts and discrete the weighted Besov spaces by the discretization method. Some preliminary knowledge and the main structure of this paper are outlined in the end.The following chapter considers the weighted Besov space which is constructed by the common weight function ωα(x)=(1+|x|2)α/2[x∈Rd, α>0). We first estimate the asymptotic degrees of the linear average and stochastic widths of embeddings of weighted sequence spaces. By the embedding theorem, we shift these results from the weighted sequence spaces to the weighted Besov spaces and obtain our main theorem of the compact embeddingsId:Bp1,q1s1(Rd,α)â†'Bp2,q2s2(Rd)(1≤p1,p2,q1,q2≤∞,-∞<s2<s1<∞).The third chapter investigates the asymptotic degrees of the linear average and stochastic widths of the following embeddings Id:Bp1,q1s1(Rd,ω)â†'Bp2,q2s2(Rd) in the weighted Besov space which is constructed by the general weight function ω∈W1∩W2. And the corresponding estimation is given. At last we make a comparison with the previous conclusions and list some work we are going to do in the future.