平面上的Kakeya BMO空間.pdf

1、湘潭大學(xué)碩士學(xué)位論文平面上的Kakeya BMO空間姓名：胡彩紅申請學(xué)位級別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：龍順潮20060504ABSTRACTBased on the Kakeya maximal function in the plane quoted, this paper definesa BMOδ space.Firstly, we introduce an equivalent definition of the BMOδ

2、norm.Secondly, we discuss the relation between the BMOδ space and L∞: 1. L∞is contained in the BMOδ space but is not equal to it; 2. the BMOδ norm ofthe Kakeya maximal function can be controlled by the L∞ norm of the ori

3、ginalfunction; 3. similarly, the BMOδ norm of the Hardy-Littlewood maximal functioncan be controlled by the L∞ norm of the original function.Meanwhile, we prove the complete and lattice space properties of the BMOδspace.

4、 Compared with the BMO space, if a function f belongs to the BMOδspace, then so does |f|.Moreover, we obtain the following results: 1. the (p, ∞)δ atom space iscontained in the (p, 2)δ atom space and the H1, ∞, 0 δ space

5、 is contained in theH1, 2, 0 δ space; 2. the BMOδ space is contained in the dual space of the H1 δ space;3. the H1, ∞, 0 δ space is equal to the H1 δ space and the dual space of the H1, 2, 0 δspace is contained in the BM

6、Oδ space. We explain why we cannot obtain the idealresults that the BMOδ space is the dual space of the H1 δ space and the inequalityis similar to John-Nirenberg inequality.Lastly, by comparing the BMOδ space with the BM

7、O space, we find that theBMO space is contained in the BMOδ space but is not equal to it. Additionally, iff belongs to the BMO space, then so does its Hardy-Littlewood maximal functionMf.Keywords: Kakeya type maximal fun