Specification of Fractional Poincare’ Inequalities for the Sequence Measures Generalization
American Journal of Applied Mathematics
Volume 5, Issue 3, June 2017, Pages: 57-67
Received: Oct. 13, 2016; Accepted: Nov. 8, 2016; Published: Jun. 12, 2017
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Authors
Abdelilah Kamal H. Sedeeg, Mathematics Department, Faculty of Education, Holy Quran and Islamic Sciences University, Khartoum, Sudan; Mathematics Department, Faculty of Sciences and Arts-Almikwah, Albaha University, Albaha, Saudi Arabia
Shawgy H. Abd Alla, Mathematics Department, Faculty of Sciences, Sudan University of Science and Technology, Khartoum, Sudan
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Abstract
The Fractional Poincare’ inequalities in Rn are endowed with a fairly general sequence measure. We show a control of L2 norm by a non–Local quantity. The assumption on the sequence measure is that it satisfies the classical Poincare’ inequality, with general results. We also verify quantity of the tightness at infinity provided by the control on the fractional derivative in terms of a sequence of a weight growing at infinity. The illustration goes to the generator of the Ornstein-Uhlenbeck semi group and some estimates of its powers.
Keywords
Poincare Inequalities, Non-Local Inequalities, Fractional Powers, Sequence Measure
To cite this article
Abdelilah Kamal H. Sedeeg, Shawgy H. Abd Alla, Specification of Fractional Poincare’ Inequalities for the Sequence Measures Generalization, American Journal of Applied Mathematics. Vol. 5, No. 3, 2017, pp. 57-67. doi: 10.11648/j.ajam.20170503.11
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Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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