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 - ∂x2f ∥ 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 - ∂x2f ∥ L2 < ∞}.

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U2 - 10.1017/S0308210500022733

DO - 10.1017/S0308210500022733

M3 - Article

AN - SCOPUS:21344465382

SN - 0308-2105

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

IS - 2

ER -