Inclusion properties of generalized Morrey spaces

Gunawan, Hendra; Hakim, Denny Ivanal; Limanta, Kevin; Masta, Al Azhary

doi:10.1002/mana.201500425

Cited by 23 publications

(22 citation statements)

References 18 publications

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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%

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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Section: Methodsmentioning

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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“…For 0 < α < n and γ > 0, we know that K α,γ ∈ L t (R n ) for n n+γ−α < t < n n−α [11]. By the inclusion property of Morrey spaces (see [6]…”

Section: The Boundedness Of I αγ On Generalized Morrey Spacesmentioning

confidence: 99%

Norm estimates for Bessel-Riesz operators on generalized Morrey spaces

Idris¹,

Gunawan²,

Eridani³

2018

Math.Boh.

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We revisit the properties of Bessel-Riesz operators and present a different proof of the boundedness of these operators on generalized Morrey spaces. We also obtain an estimate for the norm of these operators on generalized Morrey spaces in terms of the norm of their kernels on an associated Morrey space. As a consequence of our results, we reprove the boundedness of fractional integral operators on generalized Morrey spaces, especially of exponent 1, and obtain a new estimate for their norm.

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“…The subject discussion about inclusion properties of any spaces or inclusion relation between spaces has interested to study. Some authors have studied about inclusion relation in some spaces (see [1], [2], [3], [4] and [5]). It guided us to discuss the inclusion properties of other spaces.…”

Section: Introductionmentioning

confidence: 99%