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 -