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 | |