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In this paper, the author establishes inhomogeneous multi-parameter Besov and TriebelLizorkin spaces associated with different homogeneities. Moreover, the boundedness of the composition of two inhomogeneous Calderón-Zygmund singular integrals of order (ε ,σ) with different homogeneities is obtained. Mathematics subject classification (2010): 42B20, 42B35.

Inhomogeneous multi-parameter Besov and Triebel-Lizorkin spaces associated with different homogeneities and boundedness of composition operators