Abstract
The purpose of this paper is to investigate the harmonic analysis on the time scale T-q, q is an element of (0, 1) to introduce q-weighted Besov spaces subspaces of L-p(T-q) generalizing the classical one. Further, using an example of q-weighted w(alpha,beta)(.; q) which is introduced and studied. We give a new characterization of the q-Besov space using q-Poisson kernel and the g(1) Littlewood-Paley operator.