论文标题
各向异性广义的Orlicz空间中谐波分析的基本条件
A fundamental condition for harmonic analysis in anisotropic generalized Orlicz spaces
论文作者
论文摘要
在最近的许多论文中已经研究了各向异性广义的Orlicz空间，但是基本假设的理解不如各向同性情况。我们研究了各向异性$φ$ functions的最大凸小小的，并证明了两个广泛使用的条件在广义的Orlicz空间理论中，通常称为（A1）和（M）。这提供了一种更自然和易于证实的条件，可用于在各向异性广义的Orlicz空间理论中用于结果，例如詹森的不平等，我们作为推论而获得的。
Anisotropic generalized Orlicz spaces have been investigated in many recent papers, but the basic assumptions are not as well understood as in the isotropic case. We study the greatest convex minorant of anisotropic $Φ$-functions and prove the equivalence of two widely used conditions in the theory of generalized Orlicz spaces, usually called (A1) and (M). This provides a more natural and easily verifiable condition for use in the theory of anisotropic generalized Orlicz spaces for results such as Jensen's inequality which we obtain as a corollary.
