Inclusion Properties of Orlicz Spaces and Weak Orlicz Spaces Generated by Concave Functions

Taqiyuddin, Muhammad; Masta, Al Azhary

doi:10.1088/1757-899x/288/1/012103

Cited by 10 publications

(6 citation statements)

References 4 publications

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“…Theorems 2.6 and 2.7 are often called as the sufficient condition for inclusion properties of discrete Orlicz spaces. Analog results for other properties of Orlicz spaces can be found in [1,5,6,8,12,14,15,16].…”

Section: Remarksupporting

confidence: 63%

“…Moreover, they have found that two Orlicz spaces and two weak Orlicz spaces can be compared with respect to Young functions for any measurable set, although the Lebesgue space are not comparable with respect to the number . Similar results about the inclusion properties of Orlicz spaces can be found in [14,15]. Some properties of continuous Orlicz spaces, we gave as follows.…”

Section: Introductionsupporting

confidence: 67%

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Several Properties of Discrete Orlicz Spaces

Prayoga¹,

Fatimah²,

Masta³

2020

Proceedings of the Proceedings of the 7th Mathematics, Science, and Computer Science Education International Seminar, MSCEIS 20

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Introduced by Z. W. Birnbaum and W. Orlicz in 1931, Orlicz spaces are a generalization of the Lebesgue spaces. There are two kinds version of Orlicz spaces which are continuous Orlicz spaces denoted by and discrete Orlicz spaces denoted by ℓ. The properties of spaces are already known. The aim of this study is to discuss the properties of discrete Orlicz spaces. We will see that the properties of continuous Orlicz spaces are also valid in discrete Orlicz spaces. Methods in this research are by using the properties of Young function and Luxemburg Norm. The result of this research is to show that several properties of continuous Orlicz space are also valid in discrete Orlicz spaces.

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Section: Remarksupporting

confidence: 63%

Section: Introductionsupporting

confidence: 67%

Several Properties of Discrete Orlicz Spaces

Prayoga¹,

Fatimah²,

Masta³

2020

Proceedings of the Proceedings of the 7th Mathematics, Science, and Computer Science Education International Seminar, MSCEIS 20

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“…Many authors have been culminating important observations about inclusion properties of function spaces, see (Jiménez-Vargas et al, 2018;Maligranda and Matsuoka, 2015;Masta et al, 2018;Masta, 2018;Taqiyuddin and Masta, 2018;Diening, and Růžička, 2007), etc. Reports in literature (Masta et al, 2018) obtained sufficient and necessary conditions for inclusion of strong Orlicz-Morrey spaces of all versions.…”

Section: Lemma 12 Let Y Be a Young Function Andmentioning

confidence: 99%

Third Version of Weak Orlicz–Morrey Spaces and Its In-clusion Properties

Masta

Fatimah

Taqiyuddin

2019

Indonesian J. Sci. Technol

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Orlicz–Morrey spaces are generalizations of Orlicz spaces and Morrey spaces which were first introduced by Nakai. There are three versions of Orlicz–Morrey spaces. In this article, we discussed the third version of weak Orlicz–Morrey space, which is an enlargement of third version of (strong) Orlicz– Morrey space. Similar to its first version and second version, the third version of weak Orlicz-Morrey space is considered as a generalization of weak Orlicz spaces, weak Morrey spaces, and generalized weak Morrey spaces. This study investigated some properties of the third version of weak Orlicz–Morrey spaces, especially the sufficient and necessary conditions for inclusion relations between two these spaces. One of the keys to get our result is to estimate the quasi- norm of characteristics function of open balls in ℝ.

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“…There are two kinds of Lebesgue spaces which are 'continuous' Lebesgue spaces denoted by and p-summable sequence spaces denoted by ℓ . Many researchers have studied Lebesgue spaces and its generalization over a few decades [1][2][3][4][5][6][7][8][9][10][11][12]. For example, in 2016, discussed generalized Ḧlder's inequality in 'continuous' Lebesgue spaces and in 'continuous' Orlicz -Morrey spaces [7].…”

Section: Introductionmentioning

confidence: 99%