TY - JOUR
AU - KERMAUSUOR, S.
AU - KWESSI, E.
AU - DE SOUZA, G.
PY - 2019/12/31
Y2 - 2023/03/22
TI - NOTE ON A GENERALIZATION OF THE SPACE OF DERIVATIVES OF LIPSCHITZ FUNCTIONS
JF - Journal of the Nigerian Mathematical Society
JA - JNMS
VL - 38
IS - 3
SE - Articles
DO -
UR - https://ojs.ictp.it/jnms/index.php/jnms/article/view/509
SP - 469-489
AB - 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 $L_1$.
ER -