A combinatorial approach to Musielak--Orlicz spaces

Abstract

In this paper we show that, using combinatorial inequalities and Matrix-Averages, we can generate Musielak{Orlicz spaces, i.e., we prove that Ave max 1 i n xiyi (i) k xk M i , where the Orlicz functions M1;:::;Mn depend on the matrix (yij) n=1 . We also provide an approximation result for Musielak{ Orlicz norms which already in the case of Orlicz spaces turned out to be very useful.