Inhomogeneous shearlet coorbit spaces

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In this paper, we establish inhomogeneous coorbit spaces related to the continuous shearlet transform and the weighted Lebesgue spaces [Formula: see text] for certain weights [Formula: see text]. We present an inhomogeneous shearlet frame for [Formula: see text] which gives rise to a reproducing kernel [Formula: see text] that is not contained in the space [Formula: see text]. We show that the inhomogeneous shearlet coorbit spaces are Banach spaces by introducing a generalization of the approach of Fornasier, Rauhut and Ullrich.