Locally uniform convexity in Musielak-Orlicz function spaces of Bochner type endowed with the Luxemburg norm

摘要

Criteria for locally uniform convexity of Musielak-Orlicz function spaces of Bochner type equipped with the Luxemburg norm are given. We also prove that, in Musielak-Orlicz function spaces generated by locally uniformly convex Banach space, locally uniform convexity and strict convexity are equivalent.