PERLUASAN RUANG ORLICZ-MORREY VERSI NAKAI

Rifkhi Akbar Putra Rustandi, - (2024) PERLUASAN RUANG ORLICZ-MORREY VERSI NAKAI. S1 thesis, Universitas Pendidikan Indonesia.

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Official URL: https://repository.upi.edu/

Abstract

Ruang Lebesgue merupakan ruang yang banyak dikaji dan dikembangkan. Salah satunya adalah ruang Orlicz yang merupakan perumuman dari ruang Lebesgue yang dikaji oleh Z. W. Birnbaum dan W. Orlicz (1931). Selain itu, ruang Morrey juga merupakan perumuman dari ruang Lebesgue yang dikaji oleh C. B. Morrey (1938). Selanjutnya, Nakai (2006) telah membuat kajian dalam memperumum ruang Morrey. Selain mengkaji perumuman ruang Morrey, Nakai juga menggabungkan ruang tersebut dengan ruang Orlicz yang dinamakan ruang Orlicz—Morrey. Kemudian, Dermawan, dkk. (2022) mendefinisikan sebuah fungsi Young yang diperluas atau dinamakan fungsi Young diperluas. Berdasarkan hasil kajian tentang ruang Orlicz—Morrey dan fungsi Young diperluas, pada penelitian ini akan dikaji mengenai ruang Orlicz—Morrey dengan mengganti fungsi Young menjadi fungsi Young diperluas. Adapun hasil penelitian skripsi didefinisikan ruang Orlicz—Morrey diperluas, serta dikaji sifat-sifat inklusi dan ketaksamaan Hölder pada ruang tersebut. Lebesgue space is a space that is widely studied and developed. One of them is Orlicz space which is a generalization of Lebesgue space studied by Z. W. Birnbaum and W. Orlicz (1931). In addition, Morrey space is also a generalization of Lebesgue space studied by C. B. Morrey (1938). Furthermore, Nakai (2006) has made a study in generalizing Morrey spaces. In addition to studying the generalization of Morrey space, Nakai also combines the space with Orlicz space called Orlicz-Morrey space. Then, Dermawan, et al. (2022) defined an extended Young function or called the extended Young function. Based on the results of the study of Orlicz-Morrey space and extended Young's function, this research will study the Orlicz-Morrey space by changing the Young's function into an extended Young's function. The thesis research results defined the extended Orlicz-Morrey space, and studied the properties of inclusion and Hölder's inequality on the space.

Item Type: Thesis (S1)
Additional Information: ID SINTA Dosen Pembimbing: Al Azhary Masta: 6007709 Cece Kustiawan: 6674760
Uncontrolled Keywords: ruang Orlicz—Morrey diperluas, ruang Orlicz—Morrey, fungsi Young, fungsi Young diperluas, sifat Inklusi, ketaksamaan Hölder. generalized Orlicz—Morrey space, Orlicz—Morrey space, Young function, generalized Young function, Inclusion property, Hölder’s Inequality .
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Divisions: Fakultas Pendidikan Matematika dan Ilmu Pengetahuan Alam > Jurusan Pendidikan Matematika > Program Studi Matematika (non kependidikan)
Depositing User: Rifkhi Akbar Putra Rustandi
Date Deposited: 14 Sep 2024 07:59
Last Modified: 14 Sep 2024 07:59
URI: http://repository.upi.edu/id/eprint/123512

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