A maximal function characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces.
Studia Mathematica, Tome 119 (1996) no. 3, p. 219.

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We give characterizations of weighted Besov-Lipschitz and Triebel-Lizorkin spaces with A ∞ weights via a smooth kernel which satisfies “minimal” moment and Tauberian conditions. The results are stated in terms of the mixed norm of a certain maximal function of a distribution in these weighted spaces.
Classification : 46E35, 42B25
Mots-clés : Besov-Lipschitz space, Triebel-Lizorkin space, Littlewood-Paley function, Calderón representation theorem, $A_∞$ weight, Calderón representation, weighted Triebel-Lizorkin spaces, weights, space of test functions, space of tempered distributions, weighted homogeneous Besov-Lipschitz spaces, maximal function of Peetre and Triebel 
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     author = {H.-Q. Bui and M. Paluszy\'nski and M. Taibleson},
     title = {A maximal function characterization of weighted {Besov-Lipschitz} and {Triebel-Lizorkin} spaces.},
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H.-Q. Bui; M. Paluszyński; M. Taibleson. A maximal function characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces.. Studia Mathematica, Tome 119 (1996) no. 3, p. 219. https://geodesic-test.mathdoc.fr/item/STUMA_1996__119_3_216297/