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,
    Journal of Engineering and Applied Sciences,
    Volume 15,Issue 22,
    2020,
    Pages 3654-3659,
    ISSN 1816-949x,
    jeasci.2020.3654.3659,
    (https://makhillpublications.co/view-article.php?doi=jeasci.2020.3654.3659)
    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. Further, in this study we are
interested to extract Sobolev type inequality in terms of
Riesz potentials for ρ = 1 and to extend our work for weak
type estimates when ρ = 1.
    Keywords: Gagliardo-Nirenberg inequality;hardy littlewood maximal function;riesz potentials;Sobolev type inequality