$q$-integral of product of two functions

Question

How to solve $\int\limits_a^b \left[\int\limits_t^b (x-tq)_{\Re(\alpha n+\beta-1)} d_qx\right]|\phi(t)|d_qt$ and what will be the answer? Where $|q|<1$ and the function $\phi$ be in the space $L(a,b)$ of Lebesgue measurable functions on finite interval $[a,b]$ of real line $\mathbb{R}$ given by $L(a,b) = \left\{f:\|f\|_1 = \int\limits_a^b |f(t)| d_qt < \infty\right\}$ and $(x-tq)_{\Re(\alpha n+\beta-1)} = (x-tq)(x-tq^2)\ldots(x-tq^{\Re(\alpha n+\beta-1)}), \Re(\alpha,\beta)>0.$