Quasi-Norms for a Double Sequence

Abstract

The purpose of this note is to define and characterize different kinds of quasi-norms for a double sequence obtained by generalizing the l^p-norm. In particular we focus on two weak l^p-norms: successive weak l^p-norm and standard weak l^p-norm. We give upper and lower bound of the ratio of a successive weak l^p-norm to a standard weak l^p-norm for any double sequence.