University Bulletin – ISSUE No.22- Vol. (2) – June- 2020. 83 On the Bernstein inequality Samira Alamin Sulaiman )) Dept. of mathematics, Faculty of sciences, University of Zawia Abstract Chemin [] proved the inequality of Bernstein for any tempered distribution . In this paper, we will extend its proof for a bloc dyadic ̇ and We will use the Fourier transform and apply the Yong inequality for convolution. In addition, we will use the techniques of analysis in frequency space. Keywords: Dyadic decomposition, Littlewood-Paley operators, radial functions, space of Schwartz, Bernstein inequality. )) Email: samira.sulaiman@zu.edu.ly