Volume 8, Issue 5, October 2020, Page: 53-58
Gagliardo-Nirenberg Inequality as a Consequence of Pointwise Estimates for the Functions in Terms of Riesz Potential of Gradient
Sudheer Khan, College of Applied Sciences, Beijing University of Technology, Beijing, China
Wang Shu, College of Applied Sciences, Beijing University of Technology, Beijing, China
Monica Abhidha, College of Applied Sciences, Beijing University of Technology, Beijing, China
Received: Jul. 1, 2020;       Accepted: Jul. 16, 2020;       Published: Sep. 21, 2020
DOI: 10.11648/j.sjams.20200805.11      View  120      Downloads  25
Abstract
Our aim in this study is to give the Gagliardo-Nirenberg Inequality as a consequence of pointwise estimates for the function in terms of the Riesz potential of the gradient. Our aim here is to discuss boundedness of Reisz potential in term of maximal functions and to give the proof for Gagliardo-Nirenberg Inequality in term of Reisz potential. We will extend our result to discuss weak type estimate for Gagliaro-Nirenberg Sobolev inequality. Further, in this paper we are interested to extract Sobolev type inequality in terms of Riesz potentials for α is equal to one and to extend our work for weak type estimates when p is equal to one.
Keywords
Gagliardo-Nirenberg Inequality, Hardy Littlewood Maximal Function, Riesz Potential, Sobolev Type Inequality
To cite this article
Sudheer Khan, Wang Shu, Monica Abhidha, Gagliardo-Nirenberg Inequality as a Consequence of Pointwise Estimates for the Functions in Terms of Riesz Potential of Gradient, Science Journal of Applied Mathematics and Statistics. Vol. 8, No. 5, 2020, pp. 53-58. doi: 10.11648/j.sjams.20200805.11
Copyright
Copyright © 2020 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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