In this paper we show that, using combinatorial inequalities and Matrix-Averages, we can generate Musielak-Orlicz spaces, i.e., we prove that $1/\pi \sum_{ \pi} \max\limits_{ 1 \leq i \leq n} \abs{ x_i y_{ i\pi(i)}} \sim \norm{ x}_{ \Sigma M_i}$, where the Orlicz functions $M_1,...,M_n$ depend on the matrix $(y_{ ij})_{ i,j=1}^n$. We also provide an approximation result for Musielak-Orlicz norms which already in the case of Orlicz spaces turned out to be very useful.
Categories: math.FA