The endpoint case of Carleson's pointwise convergence problem for the Schrodinger equation: a.e. convergence for data in H^{n/(2(n+1))}

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Planar theorem: for every $f\in H^{1/3}(\mathbb R^2)$ there is a full-measure set $E_f$ on which the Gaussian-regularised evolution has a limit for every $0<t<1$ and converges to $f$ as $t\downarrow0$. Higher-dimensional theorem: the same for $f\in H^{n/(2(n+1))}(\mathbb R^n)$, every $n\ge3$. With Bourgain's necessary condition this gives the exact range $s\ge n/(2(n+1))$ for $n\ge2$. Not shown: the endpoint local $L^3$ maximal inequality in the plane, sharp $L^p$ maximal estimates at the endpoint in higher dimensions, or results for other dispersive equations or convergence along curves. parent of this event

The endpoint case of Carleson's pointwise convergence problem for the Schrodinger equation: a.e. convergence for data in H^{n/(2(n+1))} parent of this event

Companion: Endpoint pointwise convergence for the Schrodinger equation in higher dimensions evidence for this event

Carleson, Some analytic problems related to statistical mechanics (1980) evidence for this event

The endpoint case of Carleson's pointwise convergence problem for the Schrodinger equation: a.e. convergence for data in H^{n/(2(n+1))} evidence for this event

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