A Carleson Problem for the Boussinesq Operator  

作　　者：Dan LI Jun Feng LI 

机构地区：[1]School of Mathematics and Statistics,Beijing Technology and Business University,Beijing 100048,P.R.China [2]School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第1期119-148,共30页数学学报（英文版）

基　　金：supported by NSFC(Grant No.12071052);the Fundamental Research Funds for the Central Universities;supported by the Research Initiation Fund for Young Teachers of Beijing Technology and Business University(Grant No.QNJJ2021-02)。

摘　　要：In this paper,we show that the Boussinesq operator B_(t)f converges pointwise to its initial data.f∈H^(s)(R)as t→0 provided s≥1/4-more precisely-on one hand,by constructing a counterexample in R we discover that the optimal convergence index sc,1=1/4;on the other hand,we find that the Hausdorff dimension of the divergence set for B_(t)f isα1,b(s)={1-2s,as1/4≤s≤1/2;1,as 0<s<1/4.Moreover,a higher dimensional lift was also obtained for f being radial.

关 键 词：Carleson problem Boussinesq operator pointwise convergence Hausdorff dimension Sobolev space 

分 类 号：O177.6[理学—数学]