Hardy-Littlewood截断极大算子的L^(p)范数的连续性  

Continuity of the Lp-norm of the truncated Hardy-Littlewood maximal operator

作　　者：武嘉 魏明权 燕敦验 WU Jia;WEI Mingquan;YAN Dunyan(School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China;School of Mathematics and statistics,Xinyang Normal University,Xinyang 464000,Henan,China)

机构地区：[1]中国科学院大学数学科学学院,北京100049 [2]信阳师范学院数学与统计学院,河南信阳464000

出　　处：《中国科学院大学学报（中英文）》2024年第1期28-34,共7页Journal of University of Chinese Academy of Sciences

基　　金：Supported by the National Natural Science Foundation of China(11871452,12071052;the Natural Science Foundation of Henan(202300410338);the Nanhu Scholar Program for Young Scholars of XYNU。

摘　　要：研究截断极大算子M^(b)_(a)的L_(p)(R^(n))→L_(p)(R^(n))范数的连续性。首先,分别给出‖M^(b)_(a)‖L_(p)(R^(n))→L_(p)(R^(n))关于参数θ=b/a的左右连续性,然后证明‖M^(b)_(a)‖L_(p)(R^(n))→L_(p)(R^(n))在无穷远处的连续性。This paper focuses on the continuity of L^(p)(R^(n))→L^(p)(R^(n))-norm of the truncated Hardy-Littlewood maximal operator Mb a with two truncation parameters a and b.We first,respectively,present the left semi-continuity and right semicontinuity of‖M^(b)_(a)‖L^(p)(R^(n))→L^(p)(R^(n))with respect toθ=b/a,and then the continuity of‖M^(b)_(a)‖L^(p)(R^(n))→L^(p)(R^(n))is extended to infinity.

关 键 词：截断极大算子 连续性 L_(p)(R^(n))→L_(p)(R^(n))范数 

分 类 号：O177[理学—数学]