Lipschitz and Besov spaces in quantum calculus

The purpose of this paper is to investigate the harmonic analysis on the time scale [Formula: see text], [Formula: see text] to introduce [Formula: see text]-weighted Besov spaces subspaces of [Formula: see text] generalizing the classical one. Further, using an example of [Formula: see text]-weighted [Formula: see text] which is introduced and studied. We give a new characterization of the [Formula: see text]-Besov space using [Formula: see text]-Poisson kernel and the [Formula: see text] Littlewood–Paley operator.