an:06473173
Zbl 1331.46036
Albuquerque, Nacib; N????ez-Alarc??n, Daniel; Santos, Joedson; Serrano-Rodr??guez, Diana Marcela
Absolutely summing multilinear operators via interpolation
EN
J. Funct. Anal. 269, No. 6, 1636-1651 (2015).
00347086
2015
j
46G25 47L22 47H60
absolutely summing operators; multilinear Bohnenblust-Hille inequality; multiple summing operators
In [J. Funct. Anal. 266, No. 6, 3726-3740 (2014; Zbl 1319.46035)], \textit{N. Albuquerque} et al. used an interpolative technique to prove the sharpness of a family of inequalities of which the multilinear Bohnenblust-Hille inequality is a particular case. In this paper, the authors introduce a variation of a class of multiple summing operators and, using the technique mentioned above, prove a more general inclusion result that encompasses other known ones and allows to recover the more recent estimates of the multilinear Bohnenblust-Hille constants. Among other possible applications, their main result also gives information about the growth of the constants of variants of the Bohnenblust-Hille inequality introduced in [\textit{D. Nu??ez-Alarc??n} et al., J. Funct. Anal. 264, No. 1, 326--336 (2013; Zbl 1264.46032)].
Jamilson Ramos Campos (Jo??o Pessoa)
Zbl 1319.46035; Zbl 1264.46032