$L^p-L^q$ estimates for the solution of the Dunkl wave equation

Béchir Amri; Mohamed Gaidi

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arXiv · 1706.08952

$L^p-L^q$ estimates for the solution of the Dunkl wave equation

Béchir Amri·Mohamed Gaidi

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Abstract

In this paper, our main aim is to derive $L^p-L^q$ estimates of the solution $u_k(x,t)$ ( t fixed) of the Cauchy problem for the homogeneous linear wave equation associated to the Dunkl Laplacian $\Delta_k$, $$\Delta_ku_k(x,t)= \partial_t^2u_k (x,t),\quad \partial_tu_k(x,0)= f(x),\quad u_k(x,0)= g(x).$$ We extend to Dunkl setting the estimates given by Srichartz in \cite{Sti} for the ordinary wave equation .

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BibTeX RIS

Béchir Amri, Mohamed Gaidi. 2017-06-27. $L^p-L^q$ estimates for the solution of the Dunkl wave equation. https://arxiv.org/abs/1706.08952

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