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arXiv · 0810.4651

Endpoint maximal and smoothing estimates for Schroedinger equations

Keith M. Rogers·Andreas Seeger
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Abstract

For $α>1$ we consider the initial value problem for the dispersive equation $i\partial_t u +(-Δ)^{α/2} u= 0$. We prove an endpoint $L^p$ inequality for the maximal function $\sup_{t\in[0,1]}|u(\cdot,t)|$ with initial values in $L^p$-Sobolev spaces, for $p\in(2+4/(d+1),\infty)$. This strengthens the fixed time estimates due to Fefferman and Stein, and Miyachi. As an essential tool we establish sharp $L^p$ space-time estimates (local in time) for the same range of $p$.

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Keith M. Rogers, Andreas Seeger. 2009-05-21. Endpoint maximal and smoothing estimates for Schroedinger equations. https://arxiv.org/abs/0810.4651

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