A Combinatorial Approach to Musielak-Orlicz Spaces

2011/12/30 by Joscha Prochno, Prochno, Joscha
Mathematics · #05A20 #46B45 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:05A20 #msc:46B45

paper · pdf · doi:10.48550/arxiv.1201.0108

arxiv created 2012/08/08 · arxiv updated 2012/08/09

Abstract

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∑_π max_{1 ≤ i ≤ n} \absx_i y_iπ(i) ∼ \normx_ΣMi, where the Orlicz functions M₁,...,M_n depend on the matrix (y_ij)_i,j=1ⁿ. 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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