Characterizations of Besov-type and Triebel–Lizorkin-type spaces via maximal functions and local means

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A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces (2012, unknown): “Notice that a special case A p,q,a(R) of these results was dealt with in [100, 104].”
Generalized Morrey spaces and trace operator (2016, background): “Yang and Yuan characterized A pq (R ) in terms of the Peetre maximal operator in [87].”
Besov-Type Spaces with Variable Smoothness and Integrability (2015, background): “Various properties and equivalent characterizations of Besov-type and Triebel-Lizorkin-type spaces, including smoothness atomic, molecular or wavelet decompositions, characterizations, respectively, via differences, oscillations, Peetre maximal functions, Lusin area functions or g∗ λ functions, have”
New Characterizations of Besov-Triebel-Lizorkin-Hausdorff Spaces Including Coorbits and Wavelets (2011, background): “In [59], equivalent (quasi-)norms of the above spaces were already established via the discrete local means and the discrete Peetre maximal function of local means, which closely follows the idea of Triebel [48] (see also [49]).”