Shearlet Coorbit Theory

In this chapter, we will provide a comprehensive overview of shearlet coorbit theory. We will present an almost self-contained introduction into coorbit theory which is the basis for all our investigations. We also discuss the group theoretical background of the continuous shearlet transform, and we explain how the shearlet transform can be combined with coorbit theory. By proceeding this way we can establish new smoothness spaces, the shearlet coorbit spaces. The structure of these spaces will be discussed in detail. In particular, we derive density, embedding, and trace results for the shearlet coorbit spaces.