Azzam, Abdullah (2019) Keterbatasan operator integral fraksional dengan menggunakan ketaksamaan tipe-Hedberg. Undergraduate thesis, Universitas Islam Negeri Maulana Malik Ibrahim.
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Abstract
INDONESIA:
Pada penelitian ini, diberikan teorema mengenai sifat keterbatasan operator integral fraksional yang disebut potensial Riesz pada ruang Lebesgue tak-homogen. Teorema ini dibuktikan dengan menggunakan metode ketakasamaan Tipe-Hedberg. Selain itu dibuktikan pula ketaksamaan tipe-lemah pada ruang Morrey tak-homogen yang merupakan akibat dari keterbatasan tersebut. Berdasarkan teorema tersebut, disimpulkan bahwa operator integral fraksional potensial Riesz adalah operator yang terbatas dari ruang ke ruang , dan juga memenuhi ketaksamaan tipe lemah di ruang Lebesgue tak-homogen. Selain itu disimpulkan pula bahwa kondisi growth dapat digantikan oleh kondisi yang lebih lemah.
ENGLISH:
In this research, the boundedness theorem of fractional integral operator, which is called Riesz potential, on the non-homogeneous Lebesgue Spaces is given. The proof of the theorem use Hedberg-Type inequality. Also the proof the weak-type inequality on the non-homogeneous Morrey spaces as the consequence of the main boundedness result is given. According to the main theorem, we conclude that the Riesz potential fractional integral operator is bounded from spaces to spaces, and that it satisfies the weak-inequality on non-homogeneous spaces. Apart from that, we conclude also that the growth condition can be replaced by weaker condition.
Item Type: | Thesis (Undergraduate) | |||||||||
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Supervisor: | Rahman, Hairur and Alisah, Evawati | |||||||||
Contributors: |
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Keywords: | operator integral fraksional; ketaksamaan tipe-hedberg; fractional integral operator; hedberg-type inequality | |||||||||
Departement: | Fakultas Sains dan Teknologi > Jurusan Matematika | |||||||||
Depositing User: | Heni Kurnia Ningsih | |||||||||
Date Deposited: | 30 Apr 2020 13:50 | |||||||||
Last Modified: | 30 Apr 2020 13:50 | |||||||||
URI: | http://etheses.uin-malang.ac.id/id/eprint/15238 |
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