JournalsjemsVol. 24, No. 4pp. 1161–1188

Summability of the coefficients of a multilinear form

  • Frédéric Bayart

    Université Clermont Auvergne, Aubière, France
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Abstract

Let TT be an mm-linear form defined on a product of p\ell_p-spaces and let ΛNm\Lambda\subset\mathbb{N}^m. We investigate the best exponent ss such that the sequence of coefficients of TT belongs to s(Λ)\ell_s(\Lambda). The cases Λ=Nm\Lambda=\mathbb{N}^m and Λ\Lambda is the diagonal of Nm\mathbb{N}^m are already known. We study the intermediate cases using notions like combinatorial dimension of sets, multiple summing maps and random polynomials.

Cite this article

Frédéric Bayart, Summability of the coefficients of a multilinear form. J. Eur. Math. Soc. 24 (2022), no. 4, pp. 1161–1188

DOI 10.4171/JEMS/1109