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Dilation method and smoothing effects of solutions to the Benjamin–Ono equation

Published online by Cambridge University Press:  14 November 2011

Nako Hayashi ,
Keiichi Kato  and
Tohru Ozawa
Nako Hayashi
Affiliation:
Department of Mathematics, Faculty of Engineering, Gunma University, Kiryu 376, Japan
Keiichi Kato
Affiliation:
Department of Mathematics, Faculty of Science, Osaka University, Toyonaka 560, Japan
Tohru Ozawa
Affiliation:
Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060., Japan
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Extract

In this paper we study smoothing effects of solutions to the Benjamin–Ono equation

where H is the Hilbcrt transform defined by

We prove that if φ ∈ H2 and (x∂x)4φ then the solution u of(BO) belongs to

, where

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 2 , 1996 , pp. 273 - 285
Copyright
Copyright © Royal Society of Edinburgh 1996

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