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$%D. Yang, Besov and Triebel-Lizorkin spaces related to singular integrals with flag kernels, Rev. Mat. Complut. 22 (2009), no. 1, 253–302.%$
Let and . In this paper, the author introduces the Besov space with and the Triebel-Lizorkin space with and associated to singular integrals with flag kernels. Some basic properties, including their dual spaces, some equivalent norm characterizations via Littlewood-Paley functions, lifting properties and some embedding theorems, on these spaces are given. Moreover, the author obtains the boundedness of flag singular integrals and fractional integrals on these spaces.
Key words: Besov space, Triebel-Lizorkin space, flag singular integral, flag fractional
integral, Littlewood-Paley operator, dual space, lifting, embedding.
2000 Mathematics Subject Classification: 42B35, 42B20, 42B25, 46E35.