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The Bohnenblust-Hille inequality combined with an inequality of Helson

Authors: Daniel Carando, Andreas Defant and Pablo Sevilla-Peris
Journal: Proc. Amer. Math. Soc. 143 (2015), 5233-5238
MSC (2010): Primary 32A05; Secondary 30C10
Published electronically: September 2, 2015
MathSciNet review: 3411141
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a variant of the Bohenblust-Hille inequality which, for certain families of polynomials, leads to constants with polynomial growth in the degree.

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  • [1] Frédéric Bayart, Hardy spaces of Dirichlet series and their composition operators, Monatsh. Math. 136 (2002), no. 3, 203-236. MR 1919645 (2003i:42032),
  • [2] Frédéric Bayart, Daniel Pellegrino, and Juan B. Seoane-Sepúlveda, The Bohr radius of the $ n$-dimensional polydisk is equivalent to $ \sqrt {(\log n)/n}$, Adv. Math. 264 (2014), 726-746. MR 3250297,
  • [3] Ron C. Blei, Fractional Cartesian products of sets, Ann. Inst. Fourier (Grenoble) 29 (1979), no. 2, v, 79-105 (English, with French summary). MR 539694 (81h:43008)
  • [4] H. F. Bohnenblust and Einar Hille, On the absolute convergence of Dirichlet series, Ann. of Math. (2) 32 (1931), no. 3, 600-622. MR 1503020,
  • [5] Andreas Defant, Leonhard Frerick, Joaquim Ortega-Cerdà, Myriam Ounaïes, and Kristian Seip, The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive, Ann. of Math. (2) 174 (2011), no. 1, 485-497. MR 2811605 (2012e:32005),
  • [6] Andreas Defant, Manuel Maestre, and Ursula Schwarting, Bohr radii of vector valued holomorphic functions, Adv. Math. 231 (2012), no. 5, 2837-2857. MR 2970467,
  • [7] G. H. Hardy and J. E. Littlewood, Some properties of fractional integrals. II, Math. Z. 34 (1932), no. 1, 403-439. MR 1545260,
  • [8] Lawrence A. Harris, Bounds on the derivatives of holomorphic functions of vectors, Analyse fonctionnelle et applications (Comptes Rendus Colloq. Analyse, Inst. Mat., Univ. Federal Rio de Janeiro, Rio de Janeiro, 1972) Actualités Aci. Indust., No. 1367. Hermann, Paris, 1975, pp. 145-163. MR 0477773 (57 #17283)
  • [9] Henry Helson, Hankel forms and sums of random variables, Studia Math. 176 (2006), no. 1, 85-92. MR 2263964 (2007i:43004),
  • [10] M. Mateljević, The isoperimetric inequality in the Hardy class $ H^{1}$, Mat. Vesnik 3(16)(31) (1979), no. 2, 169-178. MR 613907 (82i:30052)
  • [11] Miodrag Mateljević, The isoperimetric inequality and some extremal problems in $ H^{1}$, Analytic functions, Kozubnik 1979 (Proc. Seventh Conf., Kozubnik, 1979), Lecture Notes in Math., vol. 798, Springer, Berlin, 1980, pp. 364-369. MR 577467 (81k:30044)
  • [12] Joel H. Shapiro, Remarks on $ F$-spaces of analytic functions, Banach spaces of analytic functions (Proc. Pelczynski Conf., Kent State Univ., Kent, Ohio, 1976) Lecture Notes in Math., Vol. 604. Springer, Berlin, 1977, pp. 107-124. MR 0487412 (58 #7050)
  • [13] Dragan Vukotić, The isoperimetric inequality and a theorem of Hardy and Littlewood, Amer. Math. Monthly 110 (2003), no. 6, 532-536. MR 1984405,

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Additional Information

Daniel Carando
Affiliation: Departamento de Matematica - Pab I, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina – and – IMAS - CONICET, Argentina

Andreas Defant
Affiliation: Institut für Mathematik, Universität Oldenburg, D-26111 Oldenburg, Germany

Pablo Sevilla-Peris
Affiliation: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain

Keywords: Bohnenblust--Hille inequality, Helson inequality, polynomials
Received by editor(s): February 7, 2014
Published electronically: September 2, 2015
Additional Notes: The first author was partially supported by CONICET-PIP 0624, PICT 2011-1456 and UBACyT 20020130100474BA
The second author was partially supported by MICINN MTM2011-22417
The third author was supported by MICINN MTM2011-22417 and UPV-SP20120700
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2015 American Mathematical Society

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