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J Inequal Appl. 2018;2018(1):34. doi: 10.1186/s13660-018-1621-2. Epub 2018 Feb 7.

Orlicz-Garling sequence spaces of difference operator and their domination in Orlicz-Lorentz spaces.

Author information

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.
3Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia.


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.


Banach space; Garling sequence space; Lorentz sequence space; Orlicz function; Subsymmetric bases; Symmetric bases

Conflict of interest statement

The authors declare that they have no competing interests.

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