论文标题
不可分割的价值Orlicz空间，第一部分
Non-separably valued Orlicz spaces, part I
论文作者
论文摘要
对于一个度量空间$ω$，我们将均匀凸的$φ\ colonω\ times x \ x \ west [0，\ infty \ right] $生成的orlicz空间理论扩展到范围Banach Space $ x $是任意的。除了解决基本结构特性（例如完整性）外，我们还表征了可分离性，反射性并代表双重空间。此表示包括$ x'$没有radon-nikodym属性或$φ$的情况。我们应用理论代表积分函数的凸结合物和Fenchel-Moreau细分，从而在具有不可分割的范围空间的功能空间上获得了第一个一般结果。为此，我们证明了对于不可分割的范围空间，我们认为，我们认为是独立的兴趣。
For a measure space $Ω$ we extend the theory of Orlicz spaces generated by an even convex integrand $φ\colon Ω\times X \to \left[ 0, \infty \right]$ to the case when the range Banach space $X$ is arbitrary. Besides settling fundamental structural properties such as completeness, we characterize separability, reflexivity and represent the dual space. This representation includes the cases when $X'$ has no Radon-Nikodym property or $φ$ is unbounded. We apply our theory to represent convex conjugates and Fenchel-Moreau subdifferentials of integral functionals, leading to the first general such result on function spaces with non-separable range space. For this, we prove a new interchange criterion between infimum and integral for non-separable range spaces, which we consider of independent interest.
