Revistes Catalanes amb Accés Obert (RACO)

Smoothness in Musielak-Orlicz spaces equipped with the Orlicz norm

Henryk Hudzik, Z. Zbaszyniak


A formula for the distance of an arbitrary element $x$ in Musielak-Orlicz space $L^\Phi$ from the subspace $E^\Phi$ of order continuous elements is given for both (the Luxemburg and the Orlicz) norms. A formula for the norm in the dual space of $L^\Phi$ is given for any of these two norms. Criteria for smooth points and smoothness in $L^\Phi$ and $E^\Phi$ equipped with the Orlicz norm are presented.

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