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Specification of Fractional Poincare’ Inequalities for the Sequence Measures Generalization

Received: 13 October 2016     Accepted: 8 November 2016     Published: 12 June 2017
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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.

Published in American Journal of Applied Mathematics (Volume 5, Issue 3)
DOI 10.11648/j.ajam.20170503.11
Page(s) 57-67
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Poincare Inequalities, Non-Local Inequalities, Fractional Powers, Sequence Measure

References
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  • APA Style

    Abdelilah Kamal H. Sedeeg, Shawgy H. Abd Alla. (2017). Specification of Fractional Poincare’ Inequalities for the Sequence Measures Generalization. American Journal of Applied Mathematics, 5(3), 57-67. https://doi.org/10.11648/j.ajam.20170503.11

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    ACS Style

    Abdelilah Kamal H. Sedeeg; Shawgy H. Abd Alla. Specification of Fractional Poincare’ Inequalities for the Sequence Measures Generalization. Am. J. Appl. Math. 2017, 5(3), 57-67. doi: 10.11648/j.ajam.20170503.11

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    AMA Style

    Abdelilah Kamal H. Sedeeg, Shawgy H. Abd Alla. Specification of Fractional Poincare’ Inequalities for the Sequence Measures Generalization. Am J Appl Math. 2017;5(3):57-67. doi: 10.11648/j.ajam.20170503.11

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  • @article{10.11648/j.ajam.20170503.11,
      author = {Abdelilah Kamal H. Sedeeg and Shawgy H. Abd Alla},
      title = {Specification of Fractional Poincare’ Inequalities for the Sequence Measures Generalization},
      journal = {American Journal of Applied Mathematics},
      volume = {5},
      number = {3},
      pages = {57-67},
      doi = {10.11648/j.ajam.20170503.11},
      url = {https://doi.org/10.11648/j.ajam.20170503.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170503.11},
      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.},
     year = {2017}
    }
    

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    AU  - Abdelilah Kamal H. Sedeeg
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    AB  - 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.
    VL  - 5
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Author Information
  • Mathematics Department, Faculty of Education, Holy Quran and Islamic Sciences University, Khartoum, Sudan

  • Mathematics Department, Faculty of Sciences, Sudan University of Science and Technology, Khartoum, Sudan

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