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We define distribution spaces of a sequence of convolutions of a set ofdistributions with smooth functions, the shearlet system. Then, we defineassociated sequence spaces and prove characterizations. We also show areproducing identity in the class of distributions. Finally, we proveSobolev-type embeddings within the shear anisotropic inhomogeneous spaces andembeddings between (classical dyadic) isotropic inhomogeneous spaces and shearanisotropic inhomogeneous spaces.

Shear Anisotropic Inhomogeneous Besov And Triebel-Lizorkin Spaces In $R^d$