Upper estimates for Gâteaux differentiability of bump functions in Orlicz–Lorentz spaces.
Upper Semi-Continuity of Convex Functions and Openness of Affine Maps.
Using boundaries to find smooth norms
The aim of this paper is to present a tool used to show that certain Banach spaces can be endowed with smooth equivalent norms. The hypothesis uses particular countable decompositions of certain subsets of , namely boundaries. Of interest is that the main result unifies two quite well known results. In the final section, some new corollaries are given.