A fundamental condition for harmonic analysis in anisotropic generalized Orlicz spaces
A fundamental condition for harmonic analysis in anisotropic generalized Orlicz spaces
复制标题
各向异性广义Orlicz空间调和分析的基本条件
DOI：
10.1007/s12220-022-01052-5
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发表时间：
2022
影响因子：
2.4
通讯作者：
P. Hasto
中科院分区：
文献类型：
--
作者：
P. Hasto
抽象的 。最近的许多论文对各向异性广义 Orlicz 空间进行了研究，但其基本假设并不像各向同性情况那样得到很好的理解。我们研究了各向异性 Φ 函数的最大凸短函数，并证明了广义 Orlicz 空间理论中两个广泛使用的条件（通常称为（A1）和（M））的等价性。这为在各向异性广义 Orlicz 空间理论中使用我们作为推论获得的詹森不等式等结果提供了一个更自然、更容易验证的条件。
A BSTRACT . 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.