Sharma Charu, Mohiuddine Syed Abdul, Raj Kuldip, Alkhaldi Ali H
1School of Mathematics, Shri Mata Vaishno Devi University, Katra, India.
2Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.
J Inequal Appl. 2018;2018(1):34. doi: 10.1186/s13660-018-1621-2. Epub 2018 Feb 7.
We introduce new classes of generalized Orlicz-Garling sequences and Orlicz-Lorentz sequences by using a sequence of Orlicz functions and difference operator. We show that the Orlicz-Garling sequence space admits a unique 1-subsymmetric basis and a 1-dominated block basic sequence in [Formula: see text]. We also make an effort to prove that every symmetric normalized block Orlicz-Garling sequence dominates an Orlicz-Lorentz sequence. Finally, we study some geometric properties of these spaces and establish some inclusion relations between spaces.
我们通过使用一列奥利奇函数和差分算子引入了广义奥利奇 - 加林序列和奥利奇 - 洛伦兹序列的新类别。我们证明了奥利奇 - 加林序列空间在[公式：见文本]中允许一个唯一的 1 - 次对称基和一个 1 - 控制块基本序列。我们还努力证明每个对称归一化块奥利奇 - 加林序列都控制一个奥利奇 - 洛伦兹序列。最后，我们研究了这些空间的一些几何性质，并建立了空间之间的一些包含关系。
