AN UPBOUND OF HAUSDORFF’S DIMENSION OF THE DIVERGENCE SET OF THE FRACTIONAL SCHRODINGER OPERATOR ON H^(s)(R^(n))  

作　　者：Dan LI Junfeng LI Jie XIAO 李丹;李俊峰;肖杰(School of Mathematics and Statistics,Beijing Technology and Business University,Beijing 100048,China;School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China;Department of Mathematics and Statistics,Memorial University,St.John’s NL A1C 5S7,Canada)

机构地区：[1]School of Mathematics and Statistics,Beijing Technology and Business University,Beijing 100048,China [2]School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China [3]Department of Mathematics and Statistics,Memorial University,St.John’s NL A1C 5S7,Canada

出　　处：《Acta Mathematica Scientia》2021年第4期1223-1249,共27页数学物理学报（B辑英文版）

基　　金：Li Dan and Li Junfeng were supported by NSFC-DFG(11761131002);NSFC(12071052);Xiao Jie was supported by NSERC of Canada(202979463102000).

摘　　要：Given n≥2 and α≥1/2,we obtained an improved upbound of Hausdorff's dimension of the fractional Schrodinger operator;that is,supf∈H^(s)(R^(n)) dim_(H){x∈R^(n):limt→0 e^(it)(-△)^(α) f(x)≠f(x)}≤n+1-2(n+1)s/n for n/2(n+1)<s≤n/2.

关 键 词：The Carleson problem divergence set the fractional Schrodinger operator Hausdorff dimension Sobolev space 

分 类 号：O177[理学—数学]