带形区域边界上L^p函数的有理逼近  

Some rational approximations of a function in L^p on the boundary

作　　者：陈占美 邓冠铁[1] 王翠巧[1] 黄华平[1] CHEN Zhanmei;DENG Guantie;WANG Cuiqiao;HUANG Huaping(School of Mathematical Sciences,Laboratory of Mathematics and Complex Systems of Ministry of Education,Beijing Normal University,100875,Beijing,China)

机构地区：[1]北京师范大学数学科学学院数学与复杂系统教育部重点实验室,北京100875

出　　处：《北京师范大学学报（自然科学版）》2018年第4期435-439,共5页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11271045)

摘　　要：证明了一个有理函数,如果它在带形区域内是一个解析函数,并且在带形区域边界上是L^p(0<p<1)可积的,那么它属于该区域上的Hardy空间.并且还证明了带形区域边界上的L^p函数可以被一个极点在{-2i,0,2i}内的有理函数依L^p范数逼近.In this paper it is proved that a rational function will be in Hardy space on the strip,if it is an analytic function on the strip and is a L^p （0〈p〈1）integrable on the strip boundary.It is additionally shown that L^p function on the boundary of the strip can be approximated by a rational function in L^p norm and its pole is contained in{-2 i,0,2 i}.

关 键 词：带形区域 HARDY空间 有理函数 逼近 

分 类 号：O174.52[理学—数学]