A Combinatorial Approach to Musielak-Orlicz Spaces

In this paper we show that, using combinatorial inequalities and Matrix-Averages, we can generate Musielak-Orlicz spaces, i.e., we prove that $1/π\sum_π \max\limits_{1 \leq i \leq n} \abs{x_i y_{iπ(i)}} \sim \norm{x}_{ΣM_i}$, 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.

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