算子有界性及BMO_函数对Carleson测度的刻画  

The bounded property of a operator and the description of Carleson measure with BMO_ function

作　　者：张斌武[1] 孟红兵[2] 

机构地区：[1]河海大学常州校区数理部,江苏常州213022 [2]陕西师范大学数学系,陕西西安710062

出　　处：《宁夏大学学报（自然科学版）》2002年第2期97-99,共3页Journal of Ningxia University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10071047);河海大学常州校区青年科研基金资助项目(CJ2000-01)

摘　　要：研究了一个算子的有界性及Carleson测度,得到了Τμ,α,s:Lp(dμ)→Lp(dμ)是有界算子的定理,并利用α(α>0)阶Carleson测度的定义以及算子理论的有关定义、定理,刻画了α阶Carleson测度与BMO 空间及BA空间的函数之间的关系,得到了用BMO 函数的不等式刻画Carleson测度的定理.By studying the bounded property of a operator and Carleson measure, a theorem that Τμ,α,s:Lp(dμ)→Lp(dμ) is bounded operator is obtained. By the definition of Carleson measure with α (α>0) order and some definitions,theorems in operator theory, the relation between Carleson measure with α order and functions in BMO space or in BA space is described. Another theorem which describes Carleson measure with α order by the integral inequality of BMO function is gained.

关 键 词：CARLESON测度 算子有界性 BMOσ↓函数 BA函数 BOREL测度 面积测度 

分 类 号：O174.12[理学—数学]