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Optimal Hardy-Littlewood type inequalities for polynomials and multilinear operators

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Abstract

In this paper we obtain quite general and definitive forms for Hardy-Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simpler and straightforward proofs and we are able to show that in most cases the exponents involved are optimal. The technique we used is a combination of probabilistic tools and of an interpolative approach; this former technique is also employed in this paper to improve the constants for vector-valued Bohnenblust-Hilletype inequalities.

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Author information

Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal da Paraíba, 58.051-900, João Pessoa, Brazil

    N. Albuquerque

  2. Laboratoire de Mathématiques, Université Blaise Pascal Campus des Cézeaux, F-63177, Aubiere Cedex, France

    F. Bayart

  3. Departamento de Matemática, Universidade Federal da Paraíba, 58.051-900, João Pessoa, Brazil

    D. Pellegrino

  4. Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas Plaza de Ciencias 3, Universidad Complutense de Madrid, Madrid, 28040, Spain

    J. B. Seoane-Sepúlveda

  5. Instituto de Ciencias Matemáticas-ICMAT, calle Nicolás Cabrera 13-15, Madrid, 28049, Spain

    J. B. Seoane-Sepúlveda

Authors
  1. N. Albuquerque
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  2. F. Bayart
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  3. D. Pellegrino
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  4. J. B. Seoane-Sepúlveda
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Corresponding author

Correspondence to N. Albuquerque.

Additional information

N. Albuquerque was supported by PDSE/CAPES 12038-13-0.

D. Pellegrino and J. B. Seoane-Sepúlveda were supported by CNPq Grant 401735/2013-3 (PVE - Linha 2).

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Albuquerque, N., Bayart, F., Pellegrino, D. et al. Optimal Hardy-Littlewood type inequalities for polynomials and multilinear operators. Isr. J. Math. 211, 197–220 (2016). https://doi.org/10.1007/s11856-015-1264-7

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  • DOI: https://doi.org/10.1007/s11856-015-1264-7

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