Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (4): 1223-1249.doi: 10.1007/s10473-021-0412-z

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AN UPBOUND OF HAUSDORFF'S DIMENSION OF THE DIVERGENCE SET OF THE FRACTIONAL SCHRÖDINGER OPERATOR ON Hs(Rn)

Dan LI1, Junfeng LI2, Jie XIAO3   

  1. 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
  • Received:2020-04-14 Revised:2020-09-18 Online:2021-08-25 Published:2021-09-01
  • Contact: Junfeng Lis E-mail:junfengli@dlut.edu.cn
  • Supported by:
    Li Dan and Li Junfeng were supported by NSFC-DFG (11761131002) and NSFC (12071052). Xiao Jie was supported by NSERC of Canada (202979463102000).

Abstract: Given n2 and α>12, we obtained an improved upbound of Hausdorff's dimension of the fractional Schrödinger operator; that is,

supfHs(Rn)dimH{xRn: limt0eit(Δ)αf(x)f(x)}n+12(n+1)sn
for n2(n+1)<sn2.

Key words: The Carleson problem, divergence set, the fractional Schrödinger operator, Hausdorff dimension, Sobolev space

CLC Number: 

  • 42B37
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