Atomic decomposition of Besov spaces with variable smoothness and integrability

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Triebel-Lizorkin-Type Spaces with Variable Exponents (2015, methodology): “D. Drihem, Atomic decomposition of Besov spaces with variable smoothness and integrability, J. Math.”
Spaces of Variable Smoothness and Integrability: Characterizations by Local Means and Ball Means of Differences (2011, background): “We thank the anonymous referee for pointing the reference [18] out to us.”
Besov-Type Spaces with Variable Smoothness and Integrability (2015, background): “Later, Drihem [17] established the atomic characterization of B s(·) p(·),q(·)(R ) and Noi et al.”