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$%H. Kempka, 2-microlocal Besov and Triebel-Lizorkin spaces of variable integrability, Rev. Mat. Complut. 22 (2009), no. 1, 227–251.%$
We introduce 2-microlocal Besov and Triebel-Lizorkin spaces with variable integrability and give a characterization by local means. These spaces cover spaces of variable exponent, spaces of variable smoothness and weighted spaces that have been studied in recent years.
Key words: Besov spaces, Triebel-Lizorkin spaces, 2-microlocal spaces, variable
smoothness, variable integrability, local means.
2000 Mathematics Subject Classification: 42B35,46E30.