The sufficient condition for inclusion properties of discrete weighted lebesgue spaces

Masta, Al Azhary; Sumiaty, Encum; Taqiyuddin, Muhammad; Pradita, Irfan

doi:10.1088/1742-6596/1013/1/012152

Cited by 4 publications

(8 citation statements)

References 10 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: 62%

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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: 62%

“…Note that, if ( ) = , then we have ℓ (ℤ ) = ℓ (ℤ ). The discussion about Lebesgue spaces can be found in [12,13].…”

Section: Introductionmentioning

confidence: 99%

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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“…To obtain the sufficient and necessary conditions for inclusion properties of ℳ #,* (ℝ ), we used the similar methods in (Gunawan et al, 2017(Gunawan et al, , 2018Masta et al, 2018 ;Masta , 2018 ;Osançlıol , 2014 ), which pay attention to the characteristic functions of open balls in ℝ , in the following lemma. Lemma 1.3 (Guliyev et al, 2017) Let Y be a Young function, $ ∈" # , and >0, then there exists a constant > 0 such that…”

Section: Methodsmentioning

confidence: 99%

“…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. In the same paper , also proved the sufficient and necessary conditions for inclusion properties of weak Orlicz -Morrey spaces of Nakai 's and Sawano -Sugano -Tanaka's 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%