Borderline Case of Traces and Extensions for Weighted Sobolev Spaces  

作　　者：Man Zi Huang Xian Tao Wang Zhuang Wang Zhi Hao Xu 

机构地区：[1]MOE-LCSM,School of Mathematics and Statistics,Hunan Normal University,Changsha,410081,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第9期1817-1833,共17页数学学报（英文版）

基　　金：partly supported by NNSF of China(Grant No.11822105);partly supported by NNSF of China(Grant Nos.12071121 and 11720101003);supported by NNSF of China(Grant No.12101226)。

摘　　要：In this paper,we study the traces and the extensions for weighted Sobolev spaces on upper half spaces when the weights reach to the borderline cases.We first give a full characterization of the existence of trace spaces for these weighted Sobolev spaces,and then study the trace parts and the extension parts between the weighted Sobolev spaces and a new kind of Besov-type spaces(on hyperplanes)which are defined by using integral averages over selected layers of dyadic cubes.

关 键 词：Sobolev space borderline case trace theorem Besov-type space Muckenhoupt A_p weight 

分 类 号：O177[理学—数学]