Annals of Functional Analysis

On summability of multilinear operators and applications

Nacib Albuquerque, Gustavo Araújo, Wasthenny Cavalcante, Tony Nogueira, Daniel Núñez, Daniel Pellegrino, and Pilar Rueda

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This article has two clear motivations, one technical and one practical. The technical motivation unifies in a single formulation a huge family of inequalities that have been produced separately over the last ninety years in different contexts. But we do not just join inequalities; our method also creates a family of inequalities that were invisible by previous approaches. The practical motivation is to show that our new approach has the strength to attack various problems. We provide new applications of our family of inequalities, continuing recent work by Maia, Nogueira, and Pellegrino.

Article information

Ann. Funct. Anal., Volume 9, Number 4 (2018), 574-590.

Received: 20 September 2018
Accepted: 29 September 2018
First available in Project Euclid: 20 October 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A63: Operator inequalities
Secondary: 47H60: Multilinear and polynomial operators [See also 46G25]

absolutely summing operators Hardy–Littlewood inequality linearization of multilinear mappings


Albuquerque, Nacib; Araújo, Gustavo; Cavalcante, Wasthenny; Nogueira, Tony; Núñez, Daniel; Pellegrino, Daniel; Rueda, Pilar. On summability of multilinear operators and applications. Ann. Funct. Anal. 9 (2018), no. 4, 574--590. doi:10.1215/20088752-2018-0026.

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