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All Journal Jurnal Matematika dan Statistika serta Aplikasinya (Jurnal MSA) Journal of Natural Sciences and Mathematics Research Jurnal Matematika UNAND Jurnal Diferensial LOSARI: Jurnal Pengabdian Kepada Masyarakat ARRUS Jurnal Pengabdian Kepada Masyarakat Jurnal Hasil-Hasil Pengabdian dan Pemberdayaan Masyarakat (JHP2M) Journal of Mathematics, Computation and Statistics (JMATHCOS) Journal of Mathematics, Statistics, and Applications Limits: Journal of Mathematics and Its Applications
Yusuf Ramadana
Universitas Negeri Makassar
Agriculture, Biological Sciences & Forestry Humanities Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Environmental Science Health Professions Languange, Linguistic, Communication & Media Library & Information Science Materials Science & Nanotechnology Mathematics Medicine & Pharmacology Physics Public Health Social Sciences Transportation Other

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Journal : Journal of Mathematics, Computation and Statistics (JMATHCOS)

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On The Boundedness Properties of the Generalized Fractional Integrals on the Generalized Weighted Morrey Spaces Ramadana, Yusuf
Journal of Mathematics, Computations and Statistics Vol. 5 No. 2 (2022): Volume 05 Nomor 02 (Oktober 2022)
Publisher : Jurusan Matematika FMIPA UNM

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Abstract

Morrey Spaces were first introduced by C.B. Morrey in 1938. Morrey space can be considered as a generalization of the Lebesgue spaces. Morrey spaces were then generalized become the generalized Morrey spaces, the weighted Morrey spaces, and the generalized weighted Morrey spaces. One of the studies on Morrey spaces is the boundedness of certain operators on the spaces. One of the operators is the fractional integral. The boundedness of fractional integrals on the classical Morrey spaces, the weighted Morrey spaces, the generalized Morrey spaces, and the generalized weighted Morrey spaces had been known. One of the extensions of fractional integrals is generalized fractional integral. The operator was bounded on the generalized Morrey spaces. The purpose of this study is to investigate the boundedness of generalized fractional integrals on the generalized weighted Morrey spaces. The weight used is Muckenhoupt class. The results obtained show that the generalized fractional integral is bounded from generalized weighted Morrey space to another generalized weighted Morrey space under some assumptions. The main result obtained then implies the boundedness of the generalized fractional maximal operator on generalized weighted Morrey spaces under the same assumptions.
Co-Authors Andika Saputra ANDIKA SAPUTRA Dwi Fitriani Rosali Izzulhaq, Agung Muhammad Abdy Muhammad Syarifuddin Rahman Rahmat Hidayat Rosali, Dwi Fitriani Syafruddin Side Syamsuddin Mas'ud Syamsuddin Mas’ud