MOHAMMAD IMAM UTOYO, 090810095 D (2012) KARAKTERISASI KETERBATASAN OPERATOR INTEGRAL FRAKSIONAL DI RUANG MORREY. Disertasi thesis, UNIVERSITAS AIRLANGGA.

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Abstract
From previous researches on boundedness of fractional integral whether on Euclidean and quasi metric spaces (homogeneous and non homogeneous) have resulted in general of the form implication theorems and some of them in the form biimplication theorems. On the resulted theorem of the form implication are naturally arising therefrom question about the converse of its theorems. Underlying on this question to be topic of this dissertation. Therefore, study about converse of the previously resulted theorems to be the first focus of dissertation.Next, we intensively study to find new properties of boundedness fractional integral which did not cover by previous researcher. To investigate of converse validity of theorem, we have to characterize the involved measure, parameter and function of operator space definition. Hence, statement of dissertation problem is how to characterize of boundedness of fractional integral in classical Morrey and generalized Morrey spaces whether on Euclidean and quasi metric spaces to obtain biimplication theorems. The method of characterization of measure, parameters, and functions on operator space in general is done by the following (1) show that characteristic function of ball is element domain of fractional integral operator, (2) determine lower bound of fractional integral of characteristic function on ball, (3) apply (1) and (2) on inequality condition of boundedness of integral operator, and (4) using the resulted estimation on (3) to find necessary condition. Using the characterization method above, in this dissertation we obtained theorems of boundedness fractional integral in the form biimplication in Lebesgue, classical Morrey, and generalized Morrey spaces on Euclidean and quasi metric spaces whether homogeneous and non homogeneous
Item Type:  Thesis (Disertasi)  

Additional Information:  KKC KK Dis M 16/12 Uto k  
Uncontrolled Keywords:  Fractional integral operator, characterization, classical Morrey space, generalized Morrey space, Euclidean space, quasi metric space, homogeneous, non homogeneous.  
Subjects:  Q Science > QA Mathematics > QA1 Mathematics (General) Q Science > QA Mathematics > QA76.9.M35 Computer science  Mathematics Q Science > QA Mathematics > QA910.3 Mathematical Logic T Technology > T Technology (General) > T5757.97 Applied mathematics. Quantitative methods 

Divisions:  09. Sekolah Pasca Sarjana > Ilmu Matematika & IPA  
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Depositing User:  Nn Anisa Septiyo Ningtias  
Date Deposited:  2015  
Last Modified:  05 Sep 2016 05:32  
URI:  http://repository.unair.ac.id/id/eprint/32824  
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