Shearlet smoothness spaces (Q485161)

It is well known that spaces of Besov-Sobolev type can be characterized by building blocks such as atoms, molecules, wavelets where the smoothness is reflected by the related coefficients belonging to suitable sequence spaces. The paper contributes to this topic replacing the classical building blocks by more recent and more flexible ones, in particular by shearlets and curvelets. The resulting shearlet smoothness spaces are compared with corresponding Besov spaces (two-sided embeddings).