Al Farisy, M. Husen (2019) Keterbatasan operator Bessel-Riesz di ruang Lebesgue pada hipergrup yang komutatif. Undergraduate thesis, Universitas Islam Negeri Maulana Malik Ibrahim.
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Abstract
INDONESIA :
Keterbatasan operator integral fraksional di ruang Lebesgue awalnya dibuktikan oleh Hardy, Littlewood dan Sobolev sekitar tahun 1927, yang kemudian dikenal dengan sebutan ketaksamaan Hardy-Littlewood-Sobolev. Banyak peneliti yang melanjutkan penelitian tersebut, baik melanjutkan di ruang yang lebih luas atau perluasan operator integral fraksional. Salah satunya dikembangkan oleh Moch. Idris yang menyatakan bahwa operator bessel-riesz ini terbatas pada ruang Lebesgue, ruang morrey klasik maupun morrey klasik yang diperumum.
Tujuan penelitian ini adalah membuktikan keterbatasan operator bessel-riesz pada hipergrup yang komutatif di ruang Lebesgue dimana pembuktian hasilnya serupa dengan teorema Moch. Idris tetapi dibawa ke suatu hipergrup yang komutatif. Berdasarkan keterbatasan operator maksimal dan ketaksamaan Hardy-Littlewood-Sobolev diperoleh hasil bahwa ‖I_(α,γ) ‖_(L_q )≤C‖H_(α,γ) (K,λ)‖_(M^(s,t) ) ‖f‖_(L^p ) dengan H_(α,γ) adalah kernel dari operator bessel-riesz. Pada penelitian selanjutnya, diharapkan dapat melakukan kajian untuk keterbatasana operator bessel-riesz pada hipergrup yang komutatif di ruang morrey klasik ataupun morrey klasik yang di perumum.
ENGLISH :
The Boundedness of fractional integral operators in Lebesgue space were initially proven by Hardy, Littlewood and Sobolev around 1927, which became known as the Hardy-Littlewood-Sobolev inequality. Many researchers continue the research, either continuing in the wider space or expanding fractional integral operators. One of them was developed by Moch. Idris who states that the bessel-riesz operator is bounded to the Lebesgue space, the classic morrey space and the generalized classic morrey space.
The purpose of this research is to prove the boundedness of the bessel-riesz operator on commutative hypergroup in the Lebesgue space where the proof of results is similar to the Moch. Idris theorem but was taken to a commutative hypergroup. Based on the boundedness of maximum operator and Hardy-Littlewood-Sobolev inequality the results are obtained that ‖I_(α,γ) ‖_(L_q )≤C‖H_(α,γ) (K,λ)‖_(M^(s,t) ) ‖f‖_(L^p ) with H_(α,γ) is the kernel of the bessel-riesz operator. In further research, it is expected to be able to conduct a study of the constraints of bessel-riesz operators on commutative hypergroups in the classic morrey space or the generalizes classic morrey space.
Item Type: | Thesis (Undergraduate) | |||||||||
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Supervisor: | Rahman, Hairur and Jauhari, Mohammad Nafie | |||||||||
Contributors: |
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Keywords: | hipergrup; keterbatasan operator bessel-riesz; ruang lebesgue; boundedness of bessel-riesz operator; hypergroup; lebesgue space | |||||||||
Departement: | Fakultas Sains dan Teknologi > Jurusan Matematika | |||||||||
Depositing User: | Dian Anesti | |||||||||
Date Deposited: | 21 Oct 2019 13:43 | |||||||||
Last Modified: | 21 Oct 2019 13:43 | |||||||||
URI: | http://etheses.uin-malang.ac.id/id/eprint/15077 |
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