Arkiv för Matematik

  • Ark. Mat.
  • Volume 46, Number 1 (2008), 143-151.

Sharp estimates for maximal operators associated to the wave equation

Keith M. Rogers and Paco Villarroya

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Abstract

The wave equation, ∂ttuu, in ℝn+1, considered with initial data u(x,0)=fHs(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).

Article information

Source
Ark. Mat., Volume 46, Number 1 (2008), 143-151.

Dates
Received: 30 October 2006
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907026

Digital Object Identifier
doi:10.1007/s11512-007-0063-8

Mathematical Reviews number (MathSciNet)
MR2379688

Zentralblatt MATH identifier
1142.35492

Rights
2007 © Institut Mittag-Leffler

Citation

Rogers, Keith M.; Villarroya, Paco. Sharp estimates for maximal operators associated to the wave equation. Ark. Mat. 46 (2008), no. 1, 143--151. doi:10.1007/s11512-007-0063-8. https://projecteuclid.org/euclid.afm/1485907026


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