@article{KERMAUSUOR_KWESSI_DE SOUZA_2019, title={NOTE ON A GENERALIZATION OF THE SPACE OF DERIVATIVES OF LIPSCHITZ FUNCTIONS}, volume={38}, url={https://ojs.ictp.it/jnms/index.php/jnms/article/view/509}, abstractNote={In this note, we denote by $(Lip^1)’$ the space of derivatives of Lipschitz functions of order 1. We propose a generalization of the space $(Lip^1)’$ on the interval $[0,2\pi]$ for general measures on subsets of $[0,2\pi]$ with respect to the representation of the norm. As a byproduct, we obtain H\"{o}lder’s type inequalities and duality results between the space $(Lip^1)’$ as well as its generalization, and the special atoms spaces $B$ and $B(\mu,1)$, spaces first introduced by De Souza in his PhD thesis. Another byproduct is a relation between the space $(Lip^1)’$ as well as its generalization, and the space $L_\infty$. As a result we prove that the special atom space is a simple characterization of $L_1$.}, number={3}, journal={Journal of the Nigerian Mathematical Society}, author={KERMAUSUOR, S. and KWESSI, E. and DE SOUZA, G.}, year={2019}, month={Dec.}, pages={469–489} }