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A Survey on the Study of Generalized Schrödinger Operators along Curves

Author

Listed:
  • 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)

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.

Suggested Citation

  • Wenjuan Li & Huiju Wang & Qingying Xue, 2022. "A Survey on the Study of Generalized Schrödinger Operators along Curves," Mathematics, MDPI, vol. 11(1), pages 1-8, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:8-:d:1008918
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