A Survey on the Study of Generalized Schrödinger Operators along Curves

Wenjuan Li, Huiju Wang and Qingying Xue ()
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Wenjuan Li: School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China
Huiju Wang: School of Mathematics and Statistics, Henan University, Kaifeng 475001, China
Qingying Xue: School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Mathematics, 2022, vol. 11, issue 1, 1-8

Abstract: In this survey, we review the historical development for the Carleson problem about the a.e. pointwise convergence in five aspects: the a.e. convergence for generalized Schrödinger operators along vertical lines; a.e. convergence for Schrödinger operators along arbitrary single curves; a.e. convergence for Schrödinger operators along a family of restricted curves; upper bounds of p for the L p -Schrödinger maximal estimates; and a.e. convergence rate for generalized Schrödinger operators along curves. Finally, we list some open problems which need to be addressed.

Keywords: Schrödinger operator; pointwise convergence; maximal estimate; convergence rate; tangential curves (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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