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Original Articles

Remarks on an inequality of Hardy and Littlewood

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Pages 1101-1113 | Received 10 May 2016, Published online: 21 Dec 2016

References

  • N. Albuquerque, F. Bayart, D. Pellegrino and J.B. Seoane-Sepúlveda, Sharp generalizations of the multilinear Bohnenblust-Hille inequality, J. Funct. Anal. 266 (2014), 3726–3740. doi: 10.1016/j.jfa.2013.08.013
  • N. Albuquerque, F. Bayart, D. Pellegrino and J.B. Seoane-Sepúlveda, Optimal Hardy-Littlewood type inequalities for polynomials and multilinear operators, Israel J. Math. 211(1) (2016), 197–220. doi: 10.1007/s11856-015-1264-7
  • N. Albuquerque, D. Núñez-Alarcón, J. Santos and D.M. Serrano-Rodríguez, Absolutely summing multilinear operators via interpolation, J. Funct. Anal. 269 (2015), 1636–1651. doi: 10.1016/j.jfa.2015.07.001
  • G. Araújo and D. Pellegrino, Optimal Hardy-Littlewood type inequalities for m-linear forms on ℓp spaces with 1 ≤ p ≤ m, Arch. Math. (Basel) 105(3) (2015), 285–295. doi: 10.1007/s00013-015-0799-5
  • G. Badea and D. Popa, Swartz type results for nuclear and multiple 1-summing bilinear operators on c0 (X) × c0 (Y ) , Positivity 19(3) (2015), 475–487. doi: 10.1007/s11117-014-0310-8
  • A. Benedek and R. Panzone, The space Lp with mixed norm, Duke Math. J. 28 (1961), 301–324. doi: 10.1215/S0012-7094-61-02828-9
  • O. Blasco, G. Botelho, D. Pellegrino and P. Rueda, Summability of multilinear mappings: Littlewood, Orlicz and beyond, Monatsh. Math. 163(2) (2011), 131–147. doi: 10.1007/s00605-010-0209-9
  • H.F. Bohnenblust and E. Hille, On the absolute convergence of Dirichlet series, Ann. of Math. 32 (1931), 600–622. doi: 10.2307/1968255
  • Y.S. Choi and S.G. Kim, The unit ball of P(2ℓ2), Arch. Math. (Basel) 71(6) (1998), 472–480. doi: 10.1007/s000130050292
  • A. Defant, J.C. Diaz, D. Garcia and M. Maestre, Unconditional basis and Gordon-Lewis constants for spaces of polynomials, J. Funct. Anal. 181 (2001), 119–145. doi: 10.1006/jfan.2000.3702
  • V. Dimant and P. Sevilla-Peris, Summation of coefficients of polynomials on ℓp spaces, Publ. Mat. 60 (2016) 289–310. doi: 10.5565/PUBLMAT_60216_02
  • G. Hardy and J.E. Littlewood, Bilinear forms bounded in space [p, q], Quart. J. Math. 5 (1934), 241–254. doi: 10.1093/qmath/os-5.1.241
  • L.A. Harris, Bounds on the derivatives of holomorphic functions of vectors, In: Comptes rendus du Colloque D’Analyse, Rio de Janeiro, 1972, (L. Nachbin, ed.), Act. Sci. et Ind., 1367, pp. 145–163, Herman, Paris, 1975.
  • J.E. Littlewood, On bounded bilinear forms in an infinite number of variables, Quart. J. (Oxford Ser.) 1 (1930), 164–174. doi: 10.1093/qmath/os-1.1.164
  • B. Osikiewicz and A. Tonge, An interpolation approach to Hardy-Littlewood inequalities for norms of operators on sequence spaces, Linear Algebra Appl. 331 (2001), 1–9. doi: 10.1016/S0024-3795(00)00184-1
  • D. Popa, Remarks on multiple summing operators on C(Ω)-spaces, Positivity 18(1) (2014), 29–39. doi: 10.1007/s11117-013-0228-6
  • T. Praciano-Pereira, On bounded multilinear forms on a class of ℓp spaces, J. Math. Anal. Appl. 81 (1981), 561–568. doi: 10.1016/0022-247X(81)90082-2

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