Third Version of Weak Orlicz–Morrey Spaces and Its Inclusion Properties
Keywords:
Weak Orlicz spaces, Weak Morrey spaces, Weak Orlicz-Morrey space of third version, Education, Inclusion propertyAbstract
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 ballsin ℝn .
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Deringoz, F., Guliyev, V. S., and Samko, S. (2015). Boundedness of the maximal operator and its commutators on vanishing generalized Orlicz-Morrey spaces. Ann. Acad. Sci. Fenn. Math, 40(2), 535-549.
Diening, L., and Růžička, M. (2007). Interpolation operators in Orlicz–Sobolev spaces. Numerische Mathematik, 107(1), 107-129.
Gala, S., Sawano, Y., and Tanaka, H. (2015). A remark on two generalized Orlicz–Morrey spaces. Journal of Approximation Theory, 198, 1-9.
Grafakos, L., He, D., Van Nguyen, H., and Yan, L. (2019). Multilinear multiplier theorems and applications. Journal of Fourier Analysis and Applications, 25(3), 959-994.
Gunawan, H., Hakim, D. I., Limanta, K. M., and Masta, A. A. (2017). Inclusion properties of generalized Morrey spaces. Mathematische Nachrichten, 290(2-3), 332- 340.
Gunawan, H., Hakim, D. I., Nakai, E., and Sawano, Y. (2018). On inclusion relation between weak Morrey spaces and Morrey spaces. Nonlinear Analysis, 168, 27-31.
Guliyev, V.S., Hasanov, S.G., Sawano Y., and Noi, T. (2017). Non-smooth atomic decompositions for generalized Orlicz -Morrey spaces of the third kind. Acta Applicandae Mathematicae, 145(1), 133-174.
Jiménez-Vargas, A., Li, L., Peralta, A. M., Wang, L., and Wang, Y. S. (2018). 2-local standard isometries on vector-valued Lipschitz function spaces. Journal of Mathematical Analysis and Applications, 461(2), 1287-1298.
Maeda, F. Y., Mizuta, Y., Ohno, T., and Shimomura, T. (2013). Boundedness of maximal operators and Sobolev ʼs inequality on Musielak –Orlicz –Morrey spaces. Bulletin des Sciences Mathématiques, 137(1), 76-96.
Maligranda, L., and Matsuoka, K. (2015). Maximal function in Beurling–Orlicz and central Morrey–Orlicz spaces. Colloquium Mathematicum, 138, 165-181.
Masta, A.A., Gunawan, H., and Setya-Budhi, W. (2016). Inclusion properties of Orlicz and weak Orlicz spaces. Journal of Mathematical and Fundamental Sciences, 14(6), 193-203.
Masta , A.A., Gunawan , H., and Setya -Budhi , W. (2017a). An inclusion property of Orlicz Morrey spaces. Journal of Physics: Conference Series, 893(1), 012015
Masta , A. A., Gunawan , H., and Setya -Budhi , W. (2017 b). On inclusion properties of two versions ofOrlicz– Morrey spaces. Mediterranean Journal of Mathematics, 14(6), 228.
Masta, A. A. (2018). Inclusion properties of Orliczspaces and weak Orliczspaces generated by concave functions . IOP Conference Series: Materials Science and Engineering , 288 (1), 012103.
Masta, A. A., Sumiaty, E., Taqiyuddin, M., and Pradita, I. (2018). The sufficient condition for inclusion properties of discrete weighted lebesgue spaces.Journal of Physics: Conference Series, 1013(1), 012152.
Nakai, E. (2008). Orlicz–Morrey spaces and the Hardy–Littlewood maximal function. Studia Mathematica, 188, 193-221. Osançlıol, A. (2014). Inclusions between weighted Orlicz spaces. Journal of Inequalities and Applications, 2014(1), 390.
Taqiyuddin, M., and Masta, A. A. (2018). Inclusion Properties of Orlicz Spaces and Weak Orlicz Spaces Generated by Concave Functions. IOP Conference Series: Materials Science and Engineering, 288(1), 012103.
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