Sogge's local smoothing conjecture for the wave equation in three spatial dimensions

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VibeMathed record: Sogge's local smoothing conjecture for the wave equation in three spatial dimensions evidence for this event

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Sogge's local smoothing conjecture for the wave equation in three spatial dimensions evidence for this event

Sogge's local smoothing conjecture for the wave equation in three spatial dimensions parent of this event

Bochner-Riesz in three dimensions, catalogued from the same release evidence for this event

Related (family 078): Bochner-Riesz multipliers in three dimensions evidence for this event

Theorem 1.1: for every $\varepsilon>0$, $\|e^{it\sqrt{-\Delta}}f\|_{L^3(\mathbb R^3\times[1,2])}\le C_\varepsilon\|J^\varepsilon f\|_{L^3}$. With the $L^2$ and $L^\infty$-kernel endpoints, Corollary 10.6 gives the full strict range $2<p<\infty$, $\sigma>\max\{0,1-3/p\}$. Section 11, through Beltran-Hickman-Sogge, Tao and Wolff, derives the strict three-dimensional Bochner-Riesz range, maximal Bochner-Riesz bounds for $p\ge3$, the diagonal sphere restriction estimate $L^r(S^2)\to L^r(\mathbb R^3)$ for $r>3$, and the three-dimensional Kakeya maximal estimate. Not shown: the endpoint $\sigma=0$ at $p=3$, dimensions $n\ge4$, or the conjecture's general-$n$ form. parent of this event