Inclusion Properties of Orlicz and Weak Orlicz Spaces

Al Azhary Masta, Hendra Gunawan, Wono Setya Budhi


This paper discusses the structure of Orlicz spaces and weak Orlicz
spaces on n. We obtain some necessary and sufficient conditions for the inclusion property of these spaces. One of the keys is to compute the norm of the characteristic functions of the balls in n.


Inclusion property; Lebesgue spaces; Orlicz spaces; Young function; weak Orlicz spaces.

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Orlicz, W., Linear Functional Analysis (Series in Real Analysis Volume 4), World Scientific, Singapore, 1992.

Léonard, C., Orlicz Spaces, Preprint, (August 17th, 2015).

Luxemburg, W.A.J., Banach Function Spaces, Thesis, Technische Hogeschool te Delft, 1955.

Masta, A.A., On Uniform Orlicz Spaces, Thesis, Bandung Institute of Technology, 2013.

Kufner, A., John, O. & Fučik, S., Function Spaces, Noordhoff International Publishing, Czechoslovakia, 1977.

Osançliol, A., Inclusion between Weighted Orlicz Spaces, J. Inequal. Appl., 2014(390), pp. 1-8, 2014.

Rao, M.M. & Ren, Z.D., Theory of Orlicz Spaces, Monographs and Textbooks in Pure and Applied Mathematics, 146, Marcel Dekker, Inc., New York, 1991.

Welland, R., Inclusion Relations among Orlicz Spaces, Proc. Amer. Math. Soc., 17(1), pp. 135-139, 1966.

Alotaibi, A., Mursaleen, M. & Sharma, S.K., Double Sequence Spaces Over N-normed Spaces Defined by a Sequence of Orlicz Functions, J. Inequal. Appl., 2014(1), pp. 1-12, 2014.

Mursaleen, M., Raj, K. & Sharma, S.K., Some Spaces of Difference Sequences and Lacunary Statitical Convergence in N-normed Space Defined by Sequence of Orlicz Functions, Miskolc Mathematical Notes, 16(1), pp. 283-304, 2015.

Bekjan, T.N., Chen, Z., Liu, P. & Jiao, Y., Noncommutative Weak Orlicz Spaces and Martingale Inequalities, Studia Math., 204(3), pp. 195-212, 2011.

Jiao, Y., Embeddings between Weak Orlicz Martingale Spaces, J. Math. Appl., 378, pp. 220-229, 2011.

Liu N. & Ye, Y., Weak Orlicz Space and Its Convergence Theorems, Acta Math. Sci. Ser., B30(5), pp. 1492-1500, 2010.

Nakai, E., Orlicz-Morrey Spaces and Some Integral Operators, Research Report, (August 17th, 2015). bitstream/2433/26035/1/1399-13.pdf

Nakai, E., On Orlicz-Morrey Spaces, Research Report (August 17th, 2015). /1520-10.pdf

Krein, S.G., Petunīn, Y.Ī. & Semënov, E.M., Interpolation of Linear Operators, Translation of Mathematical Monograph vol. 54, American Mathematical Society, Providence, R.I., 1982.

Zhang, X. & Zhang, C., Weak Orlicz Spaces Generated by Concave Functions, International Conference on Information Science and Technology (ICIST), pp. 42-44, 2011.

Gunawan, H., Hakim, D.I., Limanta, K.M. & Masta, A.A., Inclusion Properties of Generalized Morrey Spaces, to appear in Math. Nachr, 2016.



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