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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI Journal of the Indonesian Mathematical Society Journal of Mathematical and Fundamental Sciences Indonesian Journal of Science and Technology BAREKENG: Jurnal Ilmu Matematika dan Terapan Jurnal Eurekamatika IndoMath: Indonesia Mathematics Education
Masta, Al Azhary
Universitas Pendidikan Indonesia
Humanities Astronomy Chemistry Computer Science & IT Control & Systems Engineering Earth & Planetary Sciences Economics, Econometrics & Finance Education Energy Engineering Environmental Science Industrial & Manufacturing Engineering Mathematics Mechanical Engineering Physics Transportation

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Necessary Condition for Boundedness of Stein-Weiss Operator on Orlicz-Morrey Spaces Al Hazmy, Sofihara; Masta, Al Azhary; Fatimah, Siti; Batkunde, Harmanus
Journal of the Indonesian Mathematical Society Vol. 31 No. 4 (2025): DECEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i4.1963

Abstract

This study aims to find necessary conditions for the boundedness of Stein-Weiss Operator on Orlicz-Morrey spaces. It is well known that the Orlicz-Morrey space is the generalization of the Lebesque space. In particular, by considering power function as Young’s function and zero as Morrey Space index, the Orlicz-Morrey space is a Lebesgue space itself. Orlicz-Morrey space and several operators in the space have been studied intensively by several researchers. In this study, we find a necessary condition for the boundedness of the Stein-Weiss operator on Orlicz-Morrey spaces. The technique to achieve our purpose is by substituting dilation of a radial function on a ball into inequality of boundedness assumption, and some basic properties of Young’s function. {Due to the properties of the dilation, the result will be presented as an inequality involving suitable parameters}. As a result we get the necessary condition. As a discussion, we try to find several examples that satisfy the inequalities. The most important, the result shows that there is a significant factor to see the boundedness of the Stein-Weiss operator on Orlicz-Morrey spaces. Since { Stein-Weiss operator is a generalization of fractional integral operator, the result shows that it generalize the boundedness of fractional integral on Orlicz space.
Co-Authors Amalina, Nur Dina Apriani, Meta Batkunde, Harmanus Cece Kustiawan Dasep, Dasep Encum Sumiaty, Encum Fatimah, Siti Hendra Gunawan Hulliyatul Khoiriyyah Ifronika - Indra Rukmana, Indra Khusnul Novianingsih Latifah, Afiatul Muhammad Taqiyuddin Muhammad Taqiyuddin Mulyaning Asih, Endang Cahya Nurizza, Shendy Septyaneu Pradipta Swiantana Prayoga Rizky Rosjanuardi Rosmayanti, Imalia Dwi Scarayu, Hana Mutiara Siti Fatimah Syamsul Arifin Ulfa, Nadia Wono Setya Budhi