与Hermite算子相关的算子有界性  

Boundedness of operators associated with a Hermite operator

作　　者：曹勇辉[1] 周疆[1] 

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《陕西师范大学学报（自然科学版）》2013年第5期16-18,共3页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11261055);新疆维吾尔自治区自然科学基金资助项目(2011211A005);新疆大学科研基金资助项目(BS090101;2011211A005)

摘　　要：利用权与对偶方法研究了与Hermite算子相关的乘子算子与幂算子的有界性.证明了这些算子在加权勒贝格空间有界,其中利用了与Hermite函数相关的g函数的结论,得到乘子算子与幂算子在Triebel-Lizorkin空间中是有界算子.Boundedness of multipliers and power operators associated with a Hermite operator are discussed on the Triebel-Lizoekin space. By the theory of Littlewood-Paley g function, it is proved that these operators are bounded on Lebesgue space. Based on this, it is also proved that these operators are bounded from Triebel-Lizoekin space to Triebel-Lizoekin space.

关 键 词：Hermite函数 乘子算子 幂算子 

分 类 号：O174.2[理学—数学]