Area integral,Littlewood-Paley g-function and BMOA on convex domains of finite type  

作　　者：GAO JinShou 

机构地区：[1]Department of Mathematics, Fujian Normal University, Fuzhou 350007, China

出　　处：《Science China Mathematics》2011年第10期2135-2144,共10页中国科学：数学（英文版）

基　　金：supported by Natural Science Foundation of Fujian Province (Grant No. 2009J01004)

摘　　要：Let Ω be a smoothly bounded convex domain of finite type in Cn,Ω be the boundary of Ω, S α(f) and g(f) be the area integral and Littlewood-Paley g-function on Ω,respectively. If f ∈ BMOA,then S α(f) < ∞ a.e. on Ω,and there exists a constant C such that Sα(f) ‖*≤ C ‖f‖*. The same result also holds for g(f).Let Ω be a smoothly bounded convex domain of finite type in C^n, Ω be the boundary of Ω, Sα（f） and g（f） be the area integral and Littlewood-Paley g-function on Ω, respectively. If f ∈ BMOA, then Sα（f） 〈 ∞ a.e. on Ω, and there exists a constant C such that ｜｜Sα（f）｜｜＊≤ C｜｜f｜｜＊. The same result also holds for g（f）.

关 键 词：convex domain of finite type area integral G-FUNCTION BMOA 

分 类 号：O178[理学—数学] TV698.15[理学—基础数学]