A Regularity Principle In Sequence Spaces And Applications

Keywords

Hardy–Littlewood inequalities; Multiple summing operators; Sequence spaces

Abstract

We prove a nonlinear regularity principle in sequence spaces which produces universal estimates for special series defined therein. Some consequences are obtained and, in particular, we establish new inclusion theorems for multiple summing operators. Of independent interest, we settle all Grothendieck's type (ℓ1,ℓ2) theorems for multiple summing multilinear operators. We further employ the new regularity principle to solve the classification problem concerning all pairs of admissible exponents in the anisotropic Hardy–Littlewood inequalities.

Publication Date

11-1-2017

Publication Title

Bulletin des Sciences Mathematiques

Volume

141

Issue

8

Number of Pages

802-837

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.bulsci.2017.09.001

Socpus ID

85033687220 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85033687220

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