Sifat Inklusi Dan Perumuman Ketaksamaan Hölder Pada Ruang Barisan Orlicz
Keywords:
Ketaksamaan Hölder, Ruang barisan Orlicz, Ruang Orlicz, Sifat inklusiAbstract
Orlicz spaces are a generalization of Lebesgue spaces, introduced by Z. W. Birnbaum and W. Orlicz in 1931. There are two versions of Orlicz spaces: the continuous Orlicz space and the Orlicz sequence space. The main topic of this research concerns several properties of the Orlicz sequence space. In this study, the author demonstrates the necessary and sufficient conditions for the inclusion property and the validity of Hölder's inequality in Orlicz sequence spaces. Furthermore, the author obtains the necessary and sufficient conditions for the generalization of Hölder's inequality in Orlicz sequence spaces. One of the methods used to prove these results is by utilizing the norm of characteristic sequences in Z.
Keywords: Hölder's inequality, Inclusion property, Orlicz sequence space, Orlicz space.
ABSTRAK
Ruang Orlicz adalah perumuman dari ruang Lebesgue yang dikenalkan oleh Z. W. Birnbaum dan W. Orlicz pada tahun 1931. Terdapat dua versi ruang Orlicz, yaitu ruang Orlicz kontinu dan ruang barisan Orlicz. Topik utama penelitian ini adalah mengenai beberapa sifat pada ruang barisan Orlicz. Pada penelitian ini, penulis memperlihatkan syarat cukup dan perlu sifat inklusi dan keberlakuan ketaksamaan Hölder pada ruang barisan Orlicz. Lebih jauh lagi, penulis memperoleh syarat cukup dan perlu perumuman ketaksamaan Hölder pada ruang barisan Orlicz. Salah satu cara yang digunakan untuk membuktikan hal tersebut adalah dengan menggunakan norma dari barisan karakteristik pada Z.
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