Frame Decomposition of Decomposition Spaces

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On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators (2008, methodology): “The present authors studied frame decomposition of Besov type spaces in [6].”
Shearlet Coorbit Spaces: Compactly Supported Analyzing Shearlets, Traces and Embeddings (2011, methodology): “[4] L. Borup and M. Nielsen, Frame decomposition of decomposition spaces, J. Fourier Anal.”
Wavelet transforms for homogeneous mixed-norm Triebel–Lizorkin spaces (2016, methodology): “For homogeneous Triebel–Lizorkin spaces on R we may refer the reader to works of Bownik and Ho and of Kyriazis and Petrushev [8, 26–28], and for anisotropic decompositions to papers of Borup and Nielsen and of Bownik and Ho [5, 6, 8].”
Wavelet Coorbit Spaces viewed as Decomposition Spaces (2014, methodology): “Our paper makes a strong case that this language is provided by the decomposition spaces introduced by Feichtinger and Gröbner in [8], and studied more recently in [2, 22].”
Shearlet coorbit spaces and associated Banach frames (2009, unknown): “Note that curvelet‐type decomposition spaces were considered in [ 1 ].”