Hardy's inequality in several variables (Q1840556)

The authors extend the classical Hardy inequality \[ \sum^\infty_{n=1} a^p_n\leq c_p\sum^\infty_{n=1} a^p_n, \] where \(p> 1\), \(a_n\geq 0\), and \(A_n:={1\over n}\sum^n_{j= 1} a_j\), \(c_p:= ({p\over p-1})^p\), to multiple series.