Equivalences involving $(p,q)$-multi-norms
Volume 225 / 2014
Studia Mathematica 225 (2014), 29-59
MSC: Primary 46B15; Secondary 46B28, 46B42, 47L10.
DOI: 10.4064/sm225-1-3
Abstract
We consider $(p,q)$-multi-norms and standard $t$-multi-norms based on Banach spaces of the form $L^r(\varOmega )$, and resolve some question about the mutual equivalence of two such multi-norms. We introduce a new multi-norm, called the $[p,q]$-concave multi-norm, and relate it to the standard $t$-multi-norm.
