On one class of Orlicz functions

Answering to a recent question raised by Leśnik, Maligranda, and Tomaszewski, we prove that there is an Orlicz function $Φ$ with the upper Matuszewska-Orlicz index equal to $1$ such that the Orlicz space $L_Φ$ does not satisfy Dunford-Pettis criterion of weak compactness.

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