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2016 Summation of Coefficients of Polynomials on $\ell_{p}$ Spaces
Verónica Dimant, Pablo Sevilla-Peris
Publ. Mat. 60(2): 289-310 (2016). DOI: 10.5565/PUBLMAT_60216_02


We investigate the summability of the coefficients of $m$-homogeneous polynomials and $m$-linear mappings defined on $\ell_{p}$ spaces. In our research we obtain results on the summability of the coefficients of $m$-linear mappings defined on $\ell_{p_{1}} \times \dotsb \times \ell_{p_{m}}$. The first results in this respect go back to Littlewood [17] and Bohnenblust and [6] for bilinear and $m$-linear forms on $c_{0}$, and Hardy and Littlewood [15] and Praciano-Pereira [20] for bilinear and $m$-linear forms on arbitrary $\ell_{p}$ spaces. Our results recover and in some case complete these old results through a general approach on vector valued $m$-linear mappings.


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Verónica Dimant. Pablo Sevilla-Peris. "Summation of Coefficients of Polynomials on $\ell_{p}$ Spaces." Publ. Mat. 60 (2) 289 - 310, 2016.


Received: 17 June 2014; Published: 2016
First available in Project Euclid: 11 July 2016

zbMATH: 1378.46032
MathSciNet: MR3521493
Digital Object Identifier: 10.5565/PUBLMAT_60216_02

Primary: 46G25 , 47H60‎

Keywords: Hardy-Littlewood inequalities , homogeneous polynomials , multilinear mappings , sequence spaces

Rights: Copyright © 2016 Universitat Autònoma de Barcelona, Departament de Matemàtiques


Vol.60 • No. 2 • 2016
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