Abstract
The wave equation, ∂ttu=Δu, in ℝn+1, considered with initial data u(x,0)=f∈Hs(ℝn) and u’(x,0)=0, has a solution which we denote by $\frac{1}{2}(e^{it\sqrt{-\Delta}}f+e^{-it\sqrt{-\Delta}}f)$. We give almost sharp conditions under which $\sup_{0<t<1}|e^{\pm it\sqrt{-\Delta}}f|$ and $\sup_{t\in\mathbb{R}}|e^{\pm it\sqrt{-\Delta}}f|$ are bounded from Hs(ℝn) to Lq(ℝn).
Citation
Keith M. Rogers. Paco Villarroya. "Sharp estimates for maximal operators associated to the wave equation." Ark. Mat. 46 (1) 143 - 151, April 2008. https://doi.org/10.1007/s11512-007-0063-8
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