Results in Mathematics

, 74:193 | Cite as

Sharp Anisotropic Hardy–Littlewood Inequality for Positive Multilinear Forms

  • D. Núñez-Alarcón
  • D. Pellegrino
  • D. M. Serrano-RodríguezEmail author


Using elementary techniques, we obtain the optimal anisotropic Hardy–Littlewood inequalities for positive multilinear forms. In particular, we recover an inequality proved by Bayart (J Funct Anal 274(4):1129–1154, 2018).


Multilinear forms sequence spaces Hardy–Littlewood inequalities 

Mathematics Subject Classification

47A63 47A07 



D. Pellegrino is partially supported by CNPq and Grant 2019/0014 Paraíba State Research Foundation (FAPESQ).


  1. 1.
    Araújo, G., Câmara, K.: Universal bounds for the Hardy–Littlewood inequalities on multilinear forms. Results Math. 73(3), 10 (2018). (Art. 124)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Aron, R., Núñez-Alarcón, D., Pellegrino, D., Serrano-Rodríguez, D.M.: Optimal exponents for Hardy–Littlewood inequalities for \(m\)-linear operators. Linear Algebra Appl. 531, 399–422 (2017)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bayart, F.: Multiple summing maps: coordinatewise summability, inclusion theorems and \(p\)-Sidon sets. J. Funct. Anal. 274(4), 1129–1154 (2018)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Hardy, G., Littlewood, J.E.: Bilinear forms bounded in space \([p, q]\). Q. J. Math. 5, 241–254 (1934)CrossRefGoogle Scholar
  5. 5.
    Praciano-Pereira, T.: On bounded multilinear forms on a class of \(l_{p}\) spaces. J. Math. Anal. Appl. 81(2), 561–568 (1981)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Riesz, M.: Sur les maxima des formes bilinéires et sur les fonctionnelles lineaires. Acta Math. 49, 465–497 (1926)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Santos, J., Velanga, T.: On the Bohnenblust-Hille inequality for multilinear forms. Results Math. 72(1–2), 239–244 (2017)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Schep, A.R.: Factorization of positive multilinear maps. Ill. J. Math. 28, 579–591 (1984)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • D. Núñez-Alarcón
    • 1
  • D. Pellegrino
    • 2
  • D. M. Serrano-Rodríguez
    • 1
    Email author
  1. 1.Departamento de MatemáticasUniversidad Nacional de ColombiaBogotáColombia
  2. 2.Departamento de MatemáticaUniversidade Federal da ParaíbaJoão PessoaBrazil

Personalised recommendations