Analysis · Oct 6, 2026

The exact Sobolev endpoint for Schrödinger convergence

Proves almost-everywhere convergence eitΔf→fe^{it\Delta}f\to f as t↓0t\downarrow0 for every f∈Hn/(2(n+1))(Rn)f\in H^{n/(2(n+1))}(\mathbb R^n) and every dimension n ≥ 2. This attains the sharp Sobolev equality case of Carleson's Schrödinger convergence problem, including the planar endpoint H1/3.

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