Aequationes Mathematicae ( IF 0.8 ) Pub Date : 2019-11-13 , DOI: 10.1007/s00010-019-00691-4 Radosław Kaczmarek
Strict monotonicity, lower local uniform monotonicity, upper local uniform monotonicity and their orthogonal counterparts are considered in the case of Musielak–Orlicz function spaces \(L^\Phi (\mu )\) endowed with the Mazur–Orlicz F-norm as well as in the case of their subspaces \(E^\Phi (\mu )\) with the F-norm induced from \(L^\Phi (\mu )\). The presented results generalize some of the results from Cui et al. (Aequ Math 93:311–343, 2019) and Hudzik et al. (J Nonlinear Convex Anal 17(10):1985–2011, 2016), obtained only for Orlicz spaces as well as their subspaces of order continuous elements equipped with the Mazur–Orlicz F-norm.
中文翻译:
F范式Musielak-Orlicz空间中的某些单调性
在赋予Mazur-Orlicz F-范数的Musielak-Orlicz函数空间\(L ^ \ Phi(\ mu)\)的情况下,考虑严格的单调性,较低的局部均匀单调性,较高的局部均匀单调性及其正交对应项就像它们的子空间\(E ^ \ Phi(\ mu)\)一样,具有从\(L ^ \ Phi(\ mu)\)引起的F范数。给出的结果概括了Cui等人的一些结果。(Aequ Math 93:311–343,2019)和Hudzik等人。(J非线性凸面分析17(10):1985–2011,2016),仅针对Orlicz空间及其配备了Mazur-Orlicz F-范数的有序连续元素的子空间获得。