2024-03-29T07:05:17Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/689982022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Dilation Method and smoothing Effect of Solutions to the Benjamin-ono EquationHayashi, N.Kato, K.Ozawa, T.open access410In this paper we study smoothing effects of solutions to the Benjamin-Ono equation (BO) 8tu + u8zu + H8u = O, u(O) = </J, :z: E IR, (t,:z:) E IR X IR, where H is the Hilbert transform defined by (Hf)(z) == p.v.-1 / f--dy) y. We prove that if </J E H4 and (z8z )4</J, then the solution u of (BO) belongs to Lf:c(JR\{O};H8 •-4), whereDepartment of Mathematics, Hokkaido University1994-06-01engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83394http://hdl.handle.net/2115/6899810.14943/83394Hokkaido University Preprint Series in Mathematics247217https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/68998/1/pre247.pdfapplication/pdf611.62 KB1994-06-01