dc.contributor.author Brevig, Ole Fredrik dc.contributor.author Perfekt, Karl-Mikael dc.contributor.author Seip, Kristian dc.date.accessioned 2019-09-06T10:18:48Z dc.date.available 2019-09-06T10:18:48Z dc.date.created 2019-09-03T17:20:15Z dc.date.issued 2019 dc.identifier.citation Journal für die Reine und Angewandte Mathematik. 2019, 754 179-224. nb_NO dc.identifier.issn 0075-4102 dc.identifier.uri http://hdl.handle.net/11250/2612912 dc.description.abstract For a Dirichlet series symbol g.s/ D P n 1 bnn s , the associated Volterra operator Tg acting on a Dirichlet series f .s/ D P n 1 ann s is defined by the integral f 7! Z C1 s f .w/g0 .w/ dw: We show that Tg is a bounded operator on the Hardy space Hp of Dirichlet series with 0 < p < 1 if and only if the symbol g satisfies a Carleson measure condition. When appropriately restricted to one complex variable, our condition coincides with the standard Carleson measure characterization of BMOA.D/. A further analogy with classical BMO is that exp.cjgj/ is integrable (on the infinite polytorus) for some c > 0 whenever Tg is bounded. In particular, such g belong to Hp for every p < 1. We relate the boundedness of Tg to several other BMO-type spaces: BMOA in half-planes, the dual of H1 , and the space of symbols of bounded Hankel forms. Moreover, we study symbols whose coefficients enjoy a multiplicative structure and obtain coefficient estimates for m-homogeneous symbols as well as for general symbols. Finally, we consider the action of Tg on reproducing kernels for appropriate sequences of subspaces of H2 . Our proofs employ function and operator theoretic techniques in one and several variables; a variety of number theoretic arguments are used throughout the paper in our study of special classes of symbols nb_NO dc.language.iso eng nb_NO dc.publisher De Gryuter nb_NO dc.title Volterra operators on Hardy spaces of Dirichlet series nb_NO dc.type Journal article nb_NO dc.type Peer reviewed nb_NO dc.description.version publishedVersion nb_NO dc.source.pagenumber 179-224 nb_NO dc.source.volume 754 nb_NO dc.source.journal Journal für die Reine und Angewandte Mathematik nb_NO dc.identifier.doi 10.1515/crelle-2016-0069 dc.identifier.cristin 1721180 dc.relation.project Norges forskningsråd: 275113 nb_NO dc.description.localcode © De Gruyter 2019. nb_NO cristin.unitcode 194,63,15,0 cristin.unitname Institutt for matematiske fag cristin.ispublished true cristin.fulltext postprint cristin.qualitycode 2
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