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. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Poincare Inequalities, Non-Local Inequalities, Fractional Powers, Sequence Measure
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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
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
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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Download@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}
}
TY - JOUR T1 - Specification of Fractional Poincare’ Inequalities for the Sequence Measures Generalization AU - Abdelilah Kamal H. Sedeeg AU - Shawgy H. Abd Alla Y1 - 2017/06/12 PY - 2017 N1 - https://doi.org/10.11648/j.ajam.20170503.11 DO - 10.11648/j.ajam.20170503.11 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 57 EP - 67 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20170503.11 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 IS - 3 ER -
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