The optimal constants of the mixed \((\ell_{1},\ell_{2})\)-Littlewood inequality

DOI10.1016/J.JNT.2015.08.007zbMath1431.46024OpenAlexW1835956920MaRDI QIDQ897525

Daniel M. Pellegrino

Publication date: 7 December 2015

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2015.08.007

zbMATH Keywords

absolutely summing operatorsmixed \((\ell_1, \ell_2)\)-Littlewood inequality

Mathematics Subject Classification ID

Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) (Spaces of) multilinear mappings, polynomials (46G25) Inequalities for sums, series and integrals (26D15)

Related Items (13)

The Hardy-Littlewood Inequalities in Sequence Spaces ⋮ Optimal Hardy–Littlewood inequalities uniformly bounded by a universal constant ⋮ A new estimate for the constants of an inequality due to Hardy and Littlewood ⋮ On the constants of the Bohnenblust-Hille and Hardy-Littlewood inequalities ⋮ Optimal constants for a mixed Littlewood type inequality ⋮ On the generalized Bohnenblust-Hille inequality for real scalars ⋮ The Khinchin inequality for multiple sums revisited ⋮ Towards sharp Bohnenblust–Hille constants ⋮ Polynomial and multilinear Hardy-Littlewood inequalities: analytical and numerical approaches ⋮ Optimal blow up rate for the constants of Khinchin type inequalities ⋮ On the mixed (ℓ_1,ℓ_2)-Littlewood inequalities and interpolation ⋮ The best constants in the multiple Khintchine inequality ⋮ Optimal constants of the mixed Littlewood inequalities: the complex case

Cites Work

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• The Bohr radius of the \(n\)-dimensional polydisk is equivalent to \(\sqrt{(\log n) / n}\)
• The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive
• A new multilinear insight on Littlewood's 4/3-inequality
• There exist multilinear Bohnenblust-Hille constants \((C_n)^\infty_{n=1}\) with \(\lim_{n\to \infty}(C_{n+1} -C_n)=0\)
• Sharp generalizations of the multilinear Bohnenblust-Hille inequality
• Some applications of hypercontractive inequalities in quantum information theory
• The best constants in the Khintchine inequality
• BILINEAR FORMS BOUNDED IN SPACE [p, q]
• Lower bounds for the constants in the Bohnenblust–Hille inequality: The case of real scalars

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