【摘要】 本文研究了一类特殊的Musielak-Orlicz空间Lp(x)(Ω)赋予Luxemburg范数时的严格凸性,局部一致凸性,弱局部一致凸性,中点局部一致凸性与一致凸性.利用Banach空间几何学中刻画凸性的一般方法,并结合一般Musielak-Orlicz空间凸性的判别准则,获得了用p(x)刻画空间Lp(x)(Ω)赋予Luxemburg范数时,上述几种凸性的充分必要条件.更多还原

【Abstract】 In this paper,we study rotundity,locally uniform rotundity,weakly locally uniform rotundity,mid-point locally uniform rotundity and uniform rotundity of a class of special Musielak-Orlicz spaces Lp(x)(Ω)with Luxemburg norm.By using common methods of characterizing convexity in geometry of Banach spaces and criteria for convexity in Musielak-Orlicz spaces,we give the sufficient and necessary condition of some rotundities of Lp(x)(Ω)spaces above.更多还原