  In this paper we establish inhomogeneous coorbit spaces related to the
continuous shearlet transform and the weighted Lebesgue spaces $L_{p,v}, p\geq
1,$ for certain weights $v$. We present an inhomogeneous shearlet frame for
$L_2(\mathbb{R}^d)$ which gives rise to a reproducing kernel $R_\mathfrak{F}$
that is not contained in the space $\mathcal{A}_{1,m_v}$. To show that the
inhomogeneous shearlet coorbit spaces are Banach spaces we introduce a
generalization of the approach of Fornasier, Rauhut and Ullrich.
