Short proofs of Khintchine-type inequalities for zero-one matrices (Q1185895)

If an \(m\times n\) matrix has entries either zero or one, row sums \(r_ i\) and column sums \(s_ j\) and \(\sum r_ i=\sum s_ j=h\) then in this paper it has been proved that \[ m^ pn^ qh+\sum r^ q_ i\sum s^ p_ j\geq m^ p\sum r_ i^{q+1}+n^ q\sum s_ j^{p+1} \] which reduces to [\textit{A. Khintchine}, Rec. math. Soc. math. Moscou 39, No. 3, 35-39 (1932; Zbl 0006.15803)] \(h(n+{h\over n})\geq\sum r^ 2_ i+\sum s^ 2_ j\). Finally the inequality proved earlier by \textit{F. Matúš} [Res. Report 1652, UTIA/ČSAV, Prague 1990] has been generalised.