Pointwise convergence along a tangential curve for the fractional Schrödinger equation with 0 &lt; <i>m</i> &lt; 1

Yuan, Jiye; Zhao, Tengfei

doi:10.1002/mma.7786

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Case (B): Ae Convergence For Schrödinger Operator Along Arbi...1

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2022

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“…Meanwhile, they also estimated the capacitary dimension of the divergence set. Later, Yuan-Zhao [34] extended the result for m > 1 to the case 0 < m < 1, which is sharp up to the endpoint.…”

Section: Case (B): Ae Convergence For Schrödinger Operator Along Arbi...mentioning

confidence: 78%

A Survey on the Study of Generalized Schrödinger Operators along Curves

Wang

Xue

2022

Mathematics

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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 Lp-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.

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Section: Case (B): Ae Convergence For Schrödinger Operator Along Arbi...mentioning

confidence: 78%