Optimal Hardy-Littlewood type inequalities for polynomials and multilinear operators

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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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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Keywords

  • Banach Space
  • Type Inequality
  • Multilinear Operator
  • Banach Sequence Space
  • Optimal Hardy