2024-03-28T19:08:17Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/693112022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Norms of some singular integral operators on weighted L2 spacesNakazi, T.Yamamoto, T.Singular integral operatorNormHardy spaceHelson-Szego weight(A2)condition410Let α and β be measurable functions on the unit circle T, and let W be a positive function on T such that the Ricsz projection P+ is bounded on the weighted space L2(W) on T. The singular integral operator Sa,/3 is defined by Sa,f3f = nI'+f + pI'_f, (f E L2 (W)) where I'_ = I-I'+ · Leth be an outer function such that TV= 1h12 , and let cp be an unimodular function such that cp = Ti/h. In this paper, the norm of Sa ,rJ on L2 (TV) is calculated in general, using α,β and cp. Moreover, if o; and (} are constant functions, then we give the another proof of the Feldman-Krupnik-Yiarcus theorem. If αβ belongs to the Hardy space H00 , we give the theorem which is similar to the Feldman-Krupnik-Marcus theorem.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69311info:doi/10.14943/83707https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69311/1/pre562.pdfHokkaido University Preprint Series in Mathematics5621272002-10engpublisher