J. Rákosník (ed.),
Function spaces, differential operators and nonlinear analysis.
Proceedings of the conference held in Paseky na Jizerou, September 3-9, 1995.
Mathematical Institute, Czech Academy of Sciences, and Prometheus Publishing House, Praha 1996
p. 239 - 244

Regularity properties of the solution to the wave equation in Besov spaces with $p<1$

Mircea Malarski

Mathematisches Institut, Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität, Leutragraben 1, 07743 Jena, Germany malarski@minet.uni-jena.de

Abstract: The aim of the talk is to present some regularity properties for solutions of the wave equation in $B^s_{p,q}$ with $p<1$. Up to now no such result has been known. For $p\ge 1$ a large amount of work has been done, c.f. for instance Peral, Seeger, Sogge and Mockenhaupt. The results in this paper for $p>1$ are not optimal, which can be seen comparing them with Peral's result. Whether or not our results are optimal for $p\le 1$ is open.

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