### Abstract

In this paper we study smoothing effects of solutions to the Benjamin-Ono equation (Formula Presented) where H is the Hilbert transform defined by Hf)(x) = p.v. 1/π ∫ f(y)/x - y dy. We prove that if φ ∈ H^{4} and (x∂_{x})^{4}φ, then the solution u of (BO) belongs to L_{loc}
^{∞}(ℝ\{0}; H^{8, -4}), where H^{m,s} = {f ∈ L^{2}; ∥ (1 + x^{2})^{s/2}(1 - ∂_{x}
^{2}f ∥ _{L2} < ∞}.

Original language | English |
---|---|

Pages (from-to) | 273-285 |

Number of pages | 13 |

Journal | Royal Society of Edinburgh - Proceedings A |

Volume | 126 |

Issue number | 2 |

Publication status | Published - 1996 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Royal Society of Edinburgh - Proceedings A*,

*126*(2), 273-285.

**Dilation method and smoothing effects of solutions to the Benjamin-Ono equation.** / Hayashi, Nako; Kato, Keiichi; Ozawa, Tohru.

Research output: Contribution to journal › Article

*Royal Society of Edinburgh - Proceedings A*, vol. 126, no. 2, pp. 273-285.

}

TY - JOUR

T1 - Dilation method and smoothing effects of solutions to the Benjamin-Ono equation

AU - Hayashi, Nako

AU - Kato, Keiichi

AU - Ozawa, Tohru

PY - 1996

Y1 - 1996

N2 - In this paper we study smoothing effects of solutions to the Benjamin-Ono equation (Formula Presented) where H is the Hilbert transform defined by Hf)(x) = p.v. 1/π ∫ f(y)/x - y dy. We prove that if φ ∈ H4 and (x∂x)4φ, then the solution u of (BO) belongs to Lloc ∞(ℝ\{0}; H8, -4), where Hm,s = {f ∈ L2; ∥ (1 + x2)s/2(1 - ∂x 2f ∥ L2 < ∞}.

AB - In this paper we study smoothing effects of solutions to the Benjamin-Ono equation (Formula Presented) where H is the Hilbert transform defined by Hf)(x) = p.v. 1/π ∫ f(y)/x - y dy. We prove that if φ ∈ H4 and (x∂x)4φ, then the solution u of (BO) belongs to Lloc ∞(ℝ\{0}; H8, -4), where Hm,s = {f ∈ L2; ∥ (1 + x2)s/2(1 - ∂x 2f ∥ L2 < ∞}.

UR - http://www.scopus.com/inward/record.url?scp=21344465382&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21344465382&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:21344465382

VL - 126

SP - 273

EP - 285

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 2

ER -