An embedding constant for the Hardy space of Dirichlet series
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- by Ole Fredrik Brevig PDF
- Proc. Amer. Math. Soc. 145 (2017), 1639-1641 Request permission
Abstract:
A new and simple proof of the embedding of the Hardy–Hilbert space of Dirichlet series into a conformally invariant Hardy space of the half-plane is presented, and the optimal constant of the embedding is computed.References
- G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge, at the University Press, 1952. 2d ed. MR 0046395
- Håkan Hedenmalm, Peter Lindqvist, and Kristian Seip, A Hilbert space of Dirichlet series and systems of dilated functions in $L^2(0,1)$, Duke Math. J. 86 (1997), no. 1, 1–37. MR 1427844, DOI 10.1215/S0012-7094-97-08601-4
- H. L. Montgomery and R. C. Vaughan, Hilbert’s inequality, J. London Math. Soc. (2) 8 (1974), 73–82. MR 337775, DOI 10.1112/jlms/s2-8.1.73
- Jan-Fredrik Olsen and Eero Saksman, On the boundary behaviour of the Hardy spaces of Dirichlet series and a frame bound estimate, J. Reine Angew. Math. 663 (2012), 33–66. MR 2889706, DOI 10.1515/CRELLE.2011.093
- Hervé Queffélec and Martine Queffélec, Diophantine approximation and Dirichlet series, Harish-Chandra Research Institute Lecture Notes, vol. 2, Hindustan Book Agency, New Delhi, 2013. MR 3099268
- Hervé Queffélec and Kristian Seip, Approximation numbers of composition operators on the $H^2$ space of Dirichlet series, J. Funct. Anal. 268 (2015), no. 6, 1612–1648. MR 3306358, DOI 10.1016/j.jfa.2014.11.022
Additional Information
- Ole Fredrik Brevig
- Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway
- MR Author ID: 1069722
- Email: ole.brevig@math.ntnu.no
- Received by editor(s): March 14, 2016
- Received by editor(s) in revised form: June 9, 2016
- Published electronically: October 18, 2016
- Additional Notes: The author was supported by Grant 227768 of the Research Council of Norway.
- Communicated by: Stephan Ramon Garcia
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 1639-1641
- MSC (2010): Primary 30B50; Secondary 15A63
- DOI: https://doi.org/10.1090/proc/13330
- MathSciNet review: 3601554