On the constants of the Bohnenblust-Hille and Hardy-Littlewood inequalities

DOI10.1007/s00574-016-0016-6OpenAlexW2535936893MaRDI QIDQ2400477

Gustavo S. Araújo, Daniel M. Pellegrino

Publication date: 1 September 2017

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00574-016-0016-6

zbMATH Keywords

multilinear formsHardy-Littlewood inequalityabsolutely summing operatorsBohnenblust-Hille inequality

Mathematics Subject Classification ID

Linear operator inequalities (47A63) Multilinear and polynomial operators (47H60) Evaluation of number-theoretic constants (11Y60)

Related Items

The Hardy-Littlewood Inequalities in Sequence Spaces ⋮ Optimal Hardy–Littlewood inequalities uniformly bounded by a universal constant ⋮ On the generalized Bohnenblust-Hille inequality for real scalars ⋮ Bohnenblust-Hille inequalities: analytical and computational aspects ⋮ Towards sharp Bohnenblust–Hille constants ⋮ A Gale-Berlekamp permutation-switching problem in higher dimensions ⋮ Polynomial and multilinear Hardy-Littlewood inequalities: analytical and numerical approaches ⋮ Optimal Hardy-Littlewood type inequalities for \(m\)-linear forms on \(\ell_{p}\) spaces with \({1\leq p\leq m}\) ⋮ Universal bounds for the Hardy-Littlewood inequalities on multilinear forms

Cites Work

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• Optimal Hardy-Littlewood type inequalities for polynomials and multilinear operators
• On the upper bounds for the constants of the Hardy-Littlewood inequality
• The Bohr radius of the \(n\)-dimensional polydisk is equivalent to \(\sqrt{(\log n) / n}\)
• On the best constants in the Khintchine inequality for Steinhaus variables
• A new distinguishing feature for summing, versus dominated and multiple summing operators
• The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive
• Multiple Rademacher means and their applications
• Summation of coefficients of polynomials on \(\ell_{p}\) spaces
• The spaces \(L^ p\), with mixed norm
• The optimal constants of the mixed \((\ell_{1},\ell_{2})\)-Littlewood inequality
• Coordinatewise multiple summing operators in Banach spaces
• Mixed norms and rearrangements: Sobolev's inequality and Littlewood's inequality
• On bounded multilinear forms on a class of \(l^ p \)spaces
• H. Bohr's vision of ordinary Dirichlet series; old and new results
• On the absolute convergence of Dirichlet series
• Hölder's inequality: some recent and unexpected applications
• Fully, absolutely summing and Hilbert-Schmidt multilinear mappings
• Strongly \(p\)-summing multilinear operators.
• Complex interpolation and summability properties of multilinear operators
• Absolutely \({\gamma}\)-summing multilinear operators
• Sharp generalizations of the multilinear Bohnenblust-Hille inequality
• The Bohnenblust-Hille cycle of ideas from a modern point of view
• Factorization of \textit{p}-dominated polynomials through \({L}^p\)-spaces
• A Pietsch domination theorem for \((\ell_p^s,\ell_p)\)-summing operators
• Absolutely summing multilinear operators via interpolation
• Comparing different classes of absolutely summing multilinear operators
• Blei's inequality and coordinatewise multiple summing operators
• Cohen-Kwapień type theorems for multiple summing operators
• Some applications of hypercontractive inequalities in quantum information theory
• Multiple summing operators on l_pspaces
• The best constant in the Khintchine inequality for complex Steinhaus variables, the case p=1
• The best constants in the Khintchine inequality
• Polynomial and multilinear Hardy-Littlewood inequalities: analytical and numerical approaches
• BILINEAR FORMS BOUNDED IN SPACE [p, q]
• Cohen and multiple Cohen strongly summing multilinear operators
• Absolut p-summierende Abbildungen in normierten Räumen
• Quotient Algebras of Uniform Algebras